diff --git a/doc/changelog-old.dox b/doc/changelog-old.dox
index 1ba7d039d..40a962470 100644
--- a/doc/changelog-old.dox
+++ b/doc/changelog-old.dox
@@ -510,8 +510,8 @@ No dependency changes in this release.
 -   New @ref Shaders::Generic class with common definitions, so you can
     configure mesh for the generic shader and render it with any other
     compatible shader
--   Convenience @cpp hasNormals() @ce, @cpp hasTextureCoords2D() @ce functions to
-    @ref Trade::MeshData2D and @ref Trade::MeshData3D
+-   Convenience @cpp hasNormals() @ce, @cpp hasTextureCoords2D() @ce functions
+    in @cpp Trade::MeshData2D @ce and @cpp Trade::MeshData3D @ce
 -   OpenGL ES 3.0 build now shares list of vendor extensions with OpenGL ES 2.0
     build (i.e. only those extensions that aren't part of ES 3.0 are present in
     @cpp Extensions @ce)
diff --git a/doc/changelog.dox b/doc/changelog.dox
index 04312abbe..160c07cdc 100644
--- a/doc/changelog.dox
+++ b/doc/changelog.dox
@@ -379,6 +379,8 @@ See also:
     @ref GL::DynamicAttribute::DataType::Half and @ref GL::PixelType::Half that
     are consistent with the @ref Half type used elsewhere.
 -   @cpp Trade::AbstractImporter::mesh2D() @ce,
+    @cpp Trade::MeshData2D @ce, @cpp Trade::MeshData3D @ce,
+    @cpp Trade::AbstractImporter::mesh2D() @ce,
     @cpp Trade::AbstractImporter::mesh3D() @ce and related APIs are
     deprecated in favor of @ref Trade::AbstractImporter::mesh() and the new
     @ref Trade::MeshData API. For backwards compatibility, importers
@@ -721,8 +723,8 @@ Released 2019-10-24, tagged as
     location
 -   @ref MeshTools::generateSmoothNormals() for generating weighted smooth
     normals of indexed meshes (see [mosra/magnum#229](https://github.com/mosra/magnum/pull/229))
--   @ref MeshTools::compile(const Trade::MeshData3D&, CompileFlags) now accepts
-    optional flags to control normal generation
+-   @cpp MeshTools::compile(const Trade::MeshData3D&, CompileFlags) @ce now
+    accepts optional flags to control normal generation
 
 @subsubsection changelog-2019-10-new-platform Platform libraries
 
@@ -1108,7 +1110,7 @@ Released 2019-10-24, tagged as
 -   Reading of float textures on ES3 contexts using
     @ref DebugTools::textureSubImage() returned a zero-sized image by accident
 -   @ref MeshTools::compile() was producing an incorrect mesh when
-    @ref Trade::MeshData3D had both colors and texture coordinates
+    @cpp Trade::MeshData @ce had both colors and texture coordinates
 -   Properly zero-initializing the UTF-8 buffer in
     @ref Platform::GlfwApplication::textInputEvent() (see
     [mosra/magnum#324](https://github.com/mosra/magnum/pull/324))
@@ -1514,9 +1516,9 @@ Released 2019-02-04, tagged as
     @ref GL::OpenGLTester library instead. Note that the deprecated
     `Magnum/OpenGLTester.h` header is still present, along with all other
     deprecated GL-specific headers and APIs in the project root.
--   Removed five-argument @ref Trade::MeshData2D and six-argument
-    @ref Trade::MeshData3D constructors that were deprecated since
-    February 2017. Use the full six/seven-argument versions instead.
+-   Removed five-argument @cpp Trade::MeshData2D @ce and six-argument
+    @cpp Trade::MeshData3D @ce constructors that were deprecated since February
+    2017. Use the full six/seven-argument versions instead.
 -   Removed @ref Platform application constructors taking @cpp nullptr @ce,
     deprecated in June 2016 for windowless apps and in March 2017 for windowed
     apps. Use constructors taking the @ref NoCreate tag instead.
@@ -2016,8 +2018,8 @@ Released 2018-10-23, tagged as
     clearer naming
 -   @ref MeshTools::compile() taking a @ref GL::BufferUsage and returning a
     tuple was deprecated, use the simpler version taking just
-    @ref Trade::MeshData2D / @ref Trade::MeshData3D and directly returning a
-    @ref GL::Mesh instead
+    @cpp Trade::MeshData2D @ce / @cpp Trade::MeshData3D @ce and directly
+    returning a @ref GL::Mesh instead
 -   `Shaders::VertexColor::Color` is deprecated, use the direct
     @ref Shaders::VertexColor::Color3 or @ref Shaders::VertexColor::Color4
     alternatives instead
@@ -2427,9 +2429,8 @@ Released 2018-05-01, tagged as
     In particular, @ref GL::Mesh::primitive() now returns
     @ref GL::MeshPrimitive instead of @ref Magnum::MeshPrimitive, code
     depending on the return type being implicitly convertible to
-    @ref Magnum::MeshPrimitive may break. IN all other cases,
-    @ref Trade::MeshData2D::primitive() "Trade::MeshData*D::primitive()" etc.
-    returns @ref Magnum::MeshPrimitive.
+    @ref Magnum::MeshPrimitive may break. In all other cases,
+    `Trade::MeshData*D::primitive()` etc. returns @ref Magnum::MeshPrimitive.
 -   Configuration value reader/writers are now for only
     @ref Magnum::MeshPrimitive and @ref Magnum::MeshIndexType, not for
     @ref GL::MeshPrimitive or @ref GL::MeshIndexType
@@ -2864,7 +2865,8 @@ a high-level overview.
 
 -   New @ref magnum-imageconverter "magnum-imageconverter" utility
 -   Initial implementation of @ref Trade::CameraData and @ref Trade::LightData
--   Vertex color support in @ref Trade::MeshData2D and @ref Trade::MeshData3D
+-   Vertex color support in @cpp Trade::MeshData2D @ce and
+    @cpp Trade::MeshData3D @ce
 -   @ref Trade::AbstractImageConverter member functions were changed to
     non-@cpp const @ce to make implementation of complex converter plugins possible
 -   New @ref Trade::AbstractImageConverter::exportToCompressedImage() plugin
@@ -3163,8 +3165,8 @@ a high-level overview.
 -   `Math::normalize()` and `Math::denormalize()` had confusing naming and thus
     are deprecated, use @ref Math::pack() and @ref Math::unpack() from the
     @ref Magnum/Math/Packing.h header instead
--   @ref Trade::MeshData2D and @ref Trade::MeshData3D constructors without the
-    `colors` parameter are deprecated, use the full ones instead
+-   @cpp Trade::MeshData2D @ce and @cpp Trade::MeshData3D @ce constructors
+    without the `colors` parameter are deprecated, use the full ones instead
 -   @cpp Shaders::Generic::Color @ce vertex attribute implicit constructor is
     deprecated, use a constructor with explicit component count instead
 -   The bundled @ref std::optional implementation was causing serious conflicts
diff --git a/doc/snippets/MagnumTrade.cpp b/doc/snippets/MagnumTrade.cpp
index e5cbce542..c8e681417 100644
--- a/doc/snippets/MagnumTrade.cpp
+++ b/doc/snippets/MagnumTrade.cpp
@@ -39,8 +39,6 @@
 #include "Magnum/Trade/AnimationData.h"
 #include "Magnum/Trade/ImageData.h"
 #include "Magnum/Trade/MeshData.h"
-#include "Magnum/Trade/MeshData2D.h"
-#include "Magnum/Trade/MeshData3D.h"
 #include "Magnum/Trade/ObjectData2D.h"
 #include "Magnum/Trade/ObjectData3D.h"
 #include "Magnum/Trade/PhongMaterialData.h"
@@ -50,6 +48,13 @@
 #include "Magnum/Shaders/Phong.h"
 #endif
 
+#ifdef MAGNUM_BUILD_DEPRECATED
+#define _MAGNUM_NO_DEPRECATED_MESHDATA /* So it doesn't yell here */
+
+#include "Magnum/Trade/MeshData2D.h"
+#include "Magnum/Trade/MeshData3D.h"
+#endif
+
 using namespace Magnum;
 using namespace Magnum::Math::Literals;
 
@@ -312,7 +317,9 @@ MeshTools::transformPointsInPlace(Matrix4::scaling(Vector3{2.0f}),
 /* [MeshData-usage-mutable] */
 }
 
+#ifdef MAGNUM_BUILD_DEPRECATED
 {
+CORRADE_IGNORE_DEPRECATED_PUSH
 Trade::MeshData2D& foo();
 Trade::MeshData2D& data = foo();
 /* [MeshData2D-transform] */
@@ -322,7 +329,9 @@ Matrix3 transformation =
     Matrix3::rotation(45.0_degf);
 MeshTools::transformPointsInPlace(transformation, data.positions(0));
 /* [MeshData2D-transform] */
+CORRADE_IGNORE_DEPRECATED_POP
 }
+#endif
 
 {
 Trade::ObjectData2D& baz();
@@ -335,7 +344,9 @@ Matrix3 transformation =
 static_cast<void>(transformation);
 }
 
+#ifdef MAGNUM_BUILD_DEPRECATED
 {
+CORRADE_IGNORE_DEPRECATED_PUSH
 Trade::MeshData3D& bar();
 Trade::MeshData3D& data = bar();
 /* [MeshData3D-transform] */
@@ -345,7 +356,9 @@ Matrix4 transformation =
 MeshTools::transformPointsInPlace(transformation, data.positions(0));
 MeshTools::transformVectorsInPlace(transformation, data.normals(0));
 /* [MeshData3D-transform] */
+CORRADE_IGNORE_DEPRECATED_POP
 }
+#endif
 
 {
 Trade::ObjectData3D& fizz();
diff --git a/src/Magnum/GL/Mesh.h b/src/Magnum/GL/Mesh.h
index ba6aac1ef..f3d230f99 100644
--- a/src/Magnum/GL/Mesh.h
+++ b/src/Magnum/GL/Mesh.h
@@ -196,8 +196,8 @@ layout using @ref setIndexBuffer(). You can also use @ref MeshTools::compressInd
 to conveniently compress the indices based on the range used.
 
 There is also @ref MeshTools::compile() function which operates directly on
-@ref Trade::MeshData2D / @ref Trade::MeshData3D and returns fully configured
-mesh and vertex/index buffers for use with stock shaders.
+@ref Trade::MeshData and returns fully configured mesh and vertex/index buffers
+for use with stock shaders.
 
 @attention Note that, by default, neither vertex buffers nor index buffer is
     managed (e.g. deleted on destruction) by the mesh, so you have to manage
diff --git a/src/Magnum/MeshTools/Compile.cpp b/src/Magnum/MeshTools/Compile.cpp
index 703c2f9c8..104819b96 100644
--- a/src/Magnum/MeshTools/Compile.cpp
+++ b/src/Magnum/MeshTools/Compile.cpp
@@ -27,19 +27,24 @@
 
 #include <Corrade/Containers/Optional.h>
 #include <Corrade/Containers/StridedArrayView.h>
-#include <Corrade/Containers/ArrayViewStl.h> /** @todo remove once MeshDataXD is gone */
 
 #include "Magnum/GL/Buffer.h"
 #include "Magnum/GL/Mesh.h"
 #include "Magnum/Math/Vector3.h"
-#include "Magnum/Math/Color.h"
-#include "Magnum/MeshTools/CompressIndices.h"
 #include "Magnum/MeshTools/GenerateNormals.h"
 #include "Magnum/MeshTools/Duplicate.h"
 #include "Magnum/MeshTools/Interleave.h"
 #include "Magnum/Trade/MeshData.h"
+
+#ifdef MAGNUM_BUILD_DEPRECATED
+#include <Corrade/Containers/ArrayViewStl.h>
+
+#include "Magnum/Math/Color.h"
+#include "Magnum/MeshTools/CompressIndices.h"
+#define _MAGNUM_NO_DEPRECATED_MESHDATA /* So it doesn't yell here */
 #include "Magnum/Trade/MeshData2D.h"
 #include "Magnum/Trade/MeshData3D.h"
+#endif
 
 /* This header is included only privately and doesn't introduce any linker
    dependency, thus it's completely safe */
@@ -191,6 +196,8 @@ GL::Mesh compile(const Trade::MeshData& meshData, GL::Buffer&& indices, GL::Buff
     return mesh;
 }
 
+#ifdef MAGNUM_BUILD_DEPRECATED
+CORRADE_IGNORE_DEPRECATED_PUSH
 GL::Mesh compile(const Trade::MeshData2D& meshData) {
     GL::Mesh mesh;
     mesh.setPrimitive(meshData.primitive());
@@ -264,13 +271,11 @@ GL::Mesh compile(const Trade::MeshData2D& meshData) {
     return mesh;
 }
 
-#ifdef MAGNUM_BUILD_DEPRECATED
 std::tuple<GL::Mesh, std::unique_ptr<GL::Buffer>, std::unique_ptr<GL::Buffer>> compile(const Trade::MeshData2D& meshData, GL::BufferUsage) {
     return std::make_tuple(compile(meshData),
         std::unique_ptr<GL::Buffer>{new GL::Buffer{NoCreate}},
         std::unique_ptr<GL::Buffer>{meshData.isIndexed() ? new GL::Buffer{NoCreate} : nullptr});
 }
-#endif
 
 GL::Mesh compile(const Trade::MeshData3D& meshData, CompileFlags flags) {
     GL::Mesh mesh;
@@ -426,12 +431,12 @@ GL::Mesh compile(const Trade::MeshData3D& meshData, CompileFlags flags) {
     return mesh;
 }
 
-#ifdef MAGNUM_BUILD_DEPRECATED
 std::tuple<GL::Mesh, std::unique_ptr<GL::Buffer>, std::unique_ptr<GL::Buffer>> compile(const Trade::MeshData3D& meshData, GL::BufferUsage) {
     return std::make_tuple(compile(meshData),
         std::unique_ptr<GL::Buffer>{new GL::Buffer{NoCreate}},
         std::unique_ptr<GL::Buffer>{meshData.isIndexed() ? new GL::Buffer{NoCreate} : nullptr});
 }
+CORRADE_IGNORE_DEPRECATED_POP
 #endif
 
 }}
diff --git a/src/Magnum/MeshTools/Compile.h b/src/Magnum/MeshTools/Compile.h
index 50d5e9c34..58e2a1fad 100644
--- a/src/Magnum/MeshTools/Compile.h
+++ b/src/Magnum/MeshTools/Compile.h
@@ -51,7 +51,7 @@ namespace Magnum { namespace MeshTools {
 @brief Mesh compilation flag
 @m_since{2019,10}
 
-@see @ref CompileFlags, @ref compile(const Trade::MeshData3D&, CompileFlags)
+@see @ref CompileFlags, @ref compile(const Trade::MeshData&, CompileFlags)
 */
 enum class CompileFlag: UnsignedByte {
     /**
@@ -79,7 +79,7 @@ enum class CompileFlag: UnsignedByte {
 @brief Mesh compilation flags
 @m_since{2019,10}
 
-@see @ref compile(const Trade::MeshData3D&, CompileFlags)
+@see @ref compile(const Trade::MeshData&, CompileFlags)
 */
 typedef Containers::EnumSet<CompileFlag> CompileFlags;
 
@@ -176,8 +176,11 @@ MAGNUM_MESHTOOLS_EXPORT GL::Mesh compile(const Trade::MeshData& meshData, GL::Bu
  */
 MAGNUM_MESHTOOLS_EXPORT GL::Mesh compile(const Trade::MeshData& meshData, GL::Buffer&& indices, GL::Buffer&& vertices);
 
+#ifdef MAGNUM_BUILD_DEPRECATED
 /**
 @brief Compile 2D mesh data
+@m_deprecated_since_latest Use @ref compile(const Trade::MeshData&, CompileFlags)
+    instead.
 
 Configures a mesh for @ref Shaders::Generic2D shader with vertex buffer and
 possibly also an index buffer, if the mesh is indexed. Positions are bound to
@@ -200,19 +203,23 @@ greater flexibility.
 
 @see @ref shaders-generic
 */
-MAGNUM_MESHTOOLS_EXPORT GL::Mesh compile(const Trade::MeshData2D& meshData);
+CORRADE_IGNORE_DEPRECATED_PUSH
+CORRADE_DEPRECATED("use compile(const Trade::MeshData&) instead") MAGNUM_MESHTOOLS_EXPORT GL::Mesh compile(const Trade::MeshData2D& meshData);
+CORRADE_IGNORE_DEPRECATED_POP
 
-#ifdef MAGNUM_BUILD_DEPRECATED
-/** @brief @copybrief compile(const Trade::MeshData2D&)
- * @m_deprecated_since{2018,10} Use @ref compile(const Trade::MeshData2D&)
+/** @brief Compile 2D mesh data
+ * @m_deprecated_since{2018,10} Use @ref compile(const Trade::MeshData&)
  *      instead. The @p usage parameter is ignored and returned buffer
  *      instances are empty.
  */
-CORRADE_DEPRECATED("use compile(const Trade::MeshData2D&) instead") MAGNUM_MESHTOOLS_EXPORT std::tuple<GL::Mesh, std::unique_ptr<GL::Buffer>, std::unique_ptr<GL::Buffer>> compile(const Trade::MeshData2D& meshData, GL::BufferUsage usage);
-#endif
+CORRADE_IGNORE_DEPRECATED_PUSH
+CORRADE_DEPRECATED("use compile(const Trade::MeshData&) instead") MAGNUM_MESHTOOLS_EXPORT std::tuple<GL::Mesh, std::unique_ptr<GL::Buffer>, std::unique_ptr<GL::Buffer>> compile(const Trade::MeshData2D& meshData, GL::BufferUsage usage);
+CORRADE_IGNORE_DEPRECATED_POP
 
 /**
 @brief Compile 3D mesh data
+@m_deprecated_since_latest Use @ref compile(const Trade::MeshData&, CompileFlags)
+    instead.
 
 Configures mesh for @ref Shaders::Generic3D shader with vertex buffer and
 possibly also index buffer, if the mesh is indexed. Positions are bound to
@@ -236,15 +243,18 @@ greater flexibility.
 
 @see @ref shaders-generic
 */
-MAGNUM_MESHTOOLS_EXPORT GL::Mesh compile(const Trade::MeshData3D& meshData, CompileFlags flags = {});
+CORRADE_IGNORE_DEPRECATED_PUSH
+CORRADE_DEPRECATED("use compile(const Trade::MeshData&, CompileFlags) instead") MAGNUM_MESHTOOLS_EXPORT GL::Mesh compile(const Trade::MeshData3D& meshData, CompileFlags flags = {});
+CORRADE_IGNORE_DEPRECATED_POP
 
-#ifdef MAGNUM_BUILD_DEPRECATED
-/** @brief @copybrief compile(const Trade::MeshData3D&, CompileFlags)
- * @m_deprecated_since{2018,10} Use @ref compile(const Trade::MeshData3D&, CompileFlags)
+/** @brief Compile 3D mesh data
+ * @m_deprecated_since{2018,10} Use @ref compile(const Trade::MeshData&, CompileFlags)
  *      instead. The @p usage parameter is ignored and returned buffer
  *      instances are empty.
  */
-CORRADE_DEPRECATED("use compile(const Trade::MeshData3D&) instead") MAGNUM_MESHTOOLS_EXPORT std::tuple<GL::Mesh, std::unique_ptr<GL::Buffer>, std::unique_ptr<GL::Buffer>> compile(const Trade::MeshData3D& meshData, GL::BufferUsage usage);
+CORRADE_IGNORE_DEPRECATED_PUSH
+CORRADE_DEPRECATED("use compile(const Trade::MeshData&) instead") MAGNUM_MESHTOOLS_EXPORT std::tuple<GL::Mesh, std::unique_ptr<GL::Buffer>, std::unique_ptr<GL::Buffer>> compile(const Trade::MeshData3D& meshData, GL::BufferUsage usage);
+CORRADE_IGNORE_DEPRECATED_POP
 #endif
 
 }}
diff --git a/src/Magnum/MeshTools/Test/CompileGLTest.cpp b/src/Magnum/MeshTools/Test/CompileGLTest.cpp
index 0ffc8a0e9..4257c215e 100644
--- a/src/Magnum/MeshTools/Test/CompileGLTest.cpp
+++ b/src/Magnum/MeshTools/Test/CompileGLTest.cpp
@@ -50,8 +50,14 @@
 #include "Magnum/Shaders/Phong.h"
 #include "Magnum/Shaders/VertexColor.h"
 #include "Magnum/Trade/AbstractImporter.h"
+#include "Magnum/Trade/MeshData.h"
+
+#ifdef MAGNUM_BUILD_DEPRECATED
+#define _MAGNUM_NO_DEPRECATED_MESHDATA /* So it doesn't yell here */
+
 #include "Magnum/Trade/MeshData2D.h"
 #include "Magnum/Trade/MeshData3D.h"
+#endif
 
 #include "configure.h"
 
@@ -81,6 +87,7 @@ struct CompileGLTest: GL::OpenGLTester {
     public:
         explicit CompileGLTest();
 
+        /** @todo remove the template once MeshDataXD is gone */
         template<class T> void twoDimensions();
         template<class T> void threeDimensions();
         void unknownAttribute();
@@ -169,14 +176,27 @@ constexpr Color4ub ImageData[] {
 
 CompileGLTest::CompileGLTest() {
     addInstancedTests<CompileGLTest>({
-        &CompileGLTest::twoDimensions<Trade::MeshData>,
+        &CompileGLTest::twoDimensions<Trade::MeshData>}, Containers::arraySize(Data2D));
+
+    #ifdef MAGNUM_BUILD_DEPRECATED
+    CORRADE_IGNORE_DEPRECATED_PUSH
+    addInstancedTests<CompileGLTest>({
         &CompileGLTest::twoDimensions<Trade::MeshData2D>},
         Containers::arraySize(Data2D));
+    CORRADE_IGNORE_DEPRECATED_POP
+    #endif
 
     addInstancedTests<CompileGLTest>({
-        &CompileGLTest::threeDimensions<Trade::MeshData>,
+        &CompileGLTest::threeDimensions<Trade::MeshData>},
+        Containers::arraySize(Data3D));
+
+    #ifdef MAGNUM_BUILD_DEPRECATED
+    CORRADE_IGNORE_DEPRECATED_PUSH
+    addInstancedTests<CompileGLTest>({
         &CompileGLTest::threeDimensions<Trade::MeshData3D>},
         Containers::arraySize(Data3D));
+    CORRADE_IGNORE_DEPRECATED_POP
+    #endif
 
     addTests({&CompileGLTest::unknownAttribute,
               &CompileGLTest::generateNormalsNoPosition,
@@ -224,12 +244,16 @@ template<class T> struct MeshTypeName;
 template<> struct MeshTypeName<Trade::MeshData> {
     static const char* name() { return "Trade::MeshData"; }
 };
+#ifdef MAGNUM_BUILD_DEPRECATED
+CORRADE_IGNORE_DEPRECATED_PUSH
 template<> struct MeshTypeName<Trade::MeshData2D> {
     static const char* name() { return "Trade::MeshData2D"; }
 };
 template<> struct MeshTypeName<Trade::MeshData3D> {
     static const char* name() { return "Trade::MeshData3D"; }
 };
+CORRADE_IGNORE_DEPRECATED_POP
+#endif
 
 template<class T> void CompileGLTest::twoDimensions() {
     setTestCaseTemplateName(MeshTypeName<T>::name());
@@ -297,7 +321,13 @@ template<class T> void CompileGLTest::twoDimensions() {
 
     MAGNUM_VERIFY_NO_GL_ERROR();
 
+    #ifdef MAGNUM_BUILD_DEPRECATED
+    CORRADE_IGNORE_DEPRECATED_PUSH /** @todo remove once MeshDataXD is gone */
+    #endif
     GL::Mesh mesh = compile(T{std::move(meshData)});
+    #ifdef MAGNUM_BUILD_DEPRECATED
+    CORRADE_IGNORE_DEPRECATED_POP
+    #endif
 
     MAGNUM_VERIFY_NO_GL_ERROR();
 
@@ -431,7 +461,13 @@ template<class T> void CompileGLTest::threeDimensions() {
         flags |= CompileFlag::GenerateFlatNormals;
     if(data.flags & Flag::GeneratedSmoothNormals)
         flags |= CompileFlag::GenerateSmoothNormals;
+    #ifdef MAGNUM_BUILD_DEPRECATED
+    CORRADE_IGNORE_DEPRECATED_PUSH /** @todo remove once MeshDataXD is gone */
+    #endif
     GL::Mesh mesh = compile(T{std::move(meshData)}, flags);
+    #ifdef MAGNUM_BUILD_DEPRECATED
+    CORRADE_IGNORE_DEPRECATED_POP
+    #endif
 
     MAGNUM_VERIFY_NO_GL_ERROR();
 
diff --git a/src/Magnum/Trade/AbstractImporter.cpp b/src/Magnum/Trade/AbstractImporter.cpp
index 45c0a15c7..3939dae59 100644
--- a/src/Magnum/Trade/AbstractImporter.cpp
+++ b/src/Magnum/Trade/AbstractImporter.cpp
@@ -46,6 +46,8 @@
 #include "Magnum/Trade/TextureData.h"
 
 #ifdef MAGNUM_BUILD_DEPRECATED
+#define _MAGNUM_NO_DEPRECATED_MESHDATA /* So it doesn't yell here */
+
 #include "Magnum/Trade/MeshData2D.h"
 #include "Magnum/Trade/MeshData3D.h"
 #endif
@@ -497,17 +499,17 @@ std::string AbstractImporter::mesh2DName(const UnsignedInt id) {
 
 std::string AbstractImporter::doMesh2DName(UnsignedInt) { return {}; }
 
+CORRADE_IGNORE_DEPRECATED_PUSH
 Containers::Optional<MeshData2D> AbstractImporter::mesh2D(const UnsignedInt id) {
     CORRADE_ASSERT(isOpened(), "Trade::AbstractImporter::mesh2D(): no file opened", {});
-    CORRADE_IGNORE_DEPRECATED_PUSH
     CORRADE_ASSERT(id < doMesh2DCount(), "Trade::AbstractImporter::mesh2D(): index" << id << "out of range for" << doMesh2DCount() << "entries", {});
     return doMesh2D(id);
-    CORRADE_IGNORE_DEPRECATED_POP
 }
 
 Containers::Optional<MeshData2D> AbstractImporter::doMesh2D(UnsignedInt) {
     CORRADE_ASSERT(false, "Trade::AbstractImporter::mesh2D(): not implemented", {});
 }
+CORRADE_IGNORE_DEPRECATED_POP
 
 UnsignedInt AbstractImporter::mesh3DCount() const {
     CORRADE_ASSERT(isOpened(), "Trade::AbstractImporter::mesh3DCount(): no file opened", {});
@@ -543,21 +545,19 @@ std::string AbstractImporter::doMesh3DName(const UnsignedInt id) {
     return doMeshName(id);
 }
 
+CORRADE_IGNORE_DEPRECATED_PUSH
 Containers::Optional<MeshData3D> AbstractImporter::mesh3D(const UnsignedInt id) {
     CORRADE_ASSERT(isOpened(), "Trade::AbstractImporter::mesh3D(): no file opened", {});
-    CORRADE_IGNORE_DEPRECATED_PUSH
     CORRADE_ASSERT(id < doMesh3DCount(), "Trade::AbstractImporter::mesh3D(): index" << id << "out of range for" << doMesh3DCount() << "entries", {});
     return doMesh3D(id);
-    CORRADE_IGNORE_DEPRECATED_POP
 }
 
 Containers::Optional<MeshData3D> AbstractImporter::doMesh3D(const UnsignedInt id) {
     Containers::Optional<MeshData> out = doMesh(id);
-    CORRADE_IGNORE_DEPRECATED_PUSH
     if(out) return MeshData3D{*out};
-    CORRADE_IGNORE_DEPRECATED_POP
     return Containers::NullOpt;
 }
+CORRADE_IGNORE_DEPRECATED_POP
 #endif
 
 UnsignedInt AbstractImporter::materialCount() const {
diff --git a/src/Magnum/Trade/AbstractImporter.h b/src/Magnum/Trade/AbstractImporter.h
index 29fffef87..a897e07ee 100644
--- a/src/Magnum/Trade/AbstractImporter.h
+++ b/src/Magnum/Trade/AbstractImporter.h
@@ -1049,7 +1049,7 @@ class MAGNUM_TRADE_EXPORT AbstractImporter: public PluginManager::AbstractManagi
          * @see @ref AbstractMaterialData::importerState(),
          *      @ref AnimationData::importerState(), @ref CameraData::importerState(),
          *      @ref ImageData::importerState(), @ref LightData::importerState(),
-         *      @ref MeshData2D::importerState(), @ref MeshData3D::importerState(),
+         *      @ref MeshData::importerState(),
          *      @ref ObjectData2D::importerState(), @ref ObjectData3D::importerState(),
          *      @ref SceneData::importerState(), @ref TextureData::importerState()
          */
@@ -1400,7 +1400,7 @@ class MAGNUM_TRADE_EXPORT AbstractImporter: public PluginManager::AbstractManagi
          * @brief Implementation for @ref mesh3D()
          *
          * Default implementation returns @ref doMesh() converted to
-         * @ref MeshData3D for backwards compatibility.
+         * @cpp MeshData3D @ce for backwards compatibility.
          * @m_deprecated_since_latest Implement @ref doMesh() instead.
          */
         CORRADE_IGNORE_DEPRECATED_PUSH /* Clang doesn't warn, but GCC does */
diff --git a/src/Magnum/Trade/CMakeLists.txt b/src/Magnum/Trade/CMakeLists.txt
index cf4b2a93d..09a34b12c 100644
--- a/src/Magnum/Trade/CMakeLists.txt
+++ b/src/Magnum/Trade/CMakeLists.txt
@@ -42,16 +42,6 @@ set(MagnumTrade_GracefulAssert_SRCS
     CameraData.cpp
     ImageData.cpp
     MeshData.cpp
-
-    # These have to be here instead of in MagnumTrade_SRCS because they include
-    # MeshData.h and call (and thus instantiate) various functions with inline
-    # asserts. We need the linker to pick the variant with graceful asserts for
-    # tests, and if there would be two different copies, it may happen it picks
-    # the non-graceful-assert variant, causing the tests to blow up. Happens
-    # only on the MSVC linker, but let's be safe and do this everywhere.
-    MeshData2D.cpp
-    MeshData3D.cpp
-
     ObjectData2D.cpp
     ObjectData3D.cpp
     PhongMaterialData.cpp)
@@ -67,8 +57,6 @@ set(MagnumTrade_HEADERS
     ImageData.h
     LightData.h
     MeshData.h
-    MeshData2D.h
-    MeshData3D.h
     MeshObjectData2D.h
     MeshObjectData3D.h
     ObjectData2D.h
@@ -83,6 +71,22 @@ set(MagnumTrade_HEADERS
 set(MagnumTrade_PRIVATE_HEADERS
     Implementation/arrayUtilities.h)
 
+if(MAGNUM_BUILD_DEPRECATED)
+    list(APPEND MagnumTrade_GracefulAssert_SRCS
+        # These have to be here instead of in MagnumTrade_SRCS because they
+        # include MeshData.h and call (and thus instantiate) various functions
+        # with inline asserts. We need the linker to pick the variant with
+        # graceful asserts for tests, and if there would be two different
+        # copies, it may happen it picks the non-graceful-assert variant,
+        # causing the tests to blow up. Happens only on the MSVC linker, but
+        # let's be safe and do this everywhere.
+        MeshData2D.cpp
+        MeshData3D.cpp)
+    list(APPEND MagnumTrade_HEADERS
+        MeshData2D.h
+        MeshData3D.h)
+endif()
+
 if(NOT CORRADE_PLUGINMANAGER_NO_DYNAMIC_PLUGIN_SUPPORT)
     configure_file(${CMAKE_CURRENT_SOURCE_DIR}/configure.h.cmake
                    ${CMAKE_CURRENT_BINARY_DIR}/configure.h)
diff --git a/src/Magnum/Trade/MeshData2D.cpp b/src/Magnum/Trade/MeshData2D.cpp
index ecebb7746..b534d1b3e 100644
--- a/src/Magnum/Trade/MeshData2D.cpp
+++ b/src/Magnum/Trade/MeshData2D.cpp
@@ -23,6 +23,8 @@
     DEALINGS IN THE SOFTWARE.
 */
 
+#define _MAGNUM_NO_DEPRECATED_MESHDATA /* So it doesn't yell here */
+
 #include "MeshData2D.h"
 
 #include <Corrade/Containers/ArrayViewStl.h>
@@ -64,19 +66,23 @@ MeshData2D::MeshData2D(const MeshData& other): _primitive{other.primitive()}, _i
 }
 #endif
 
+CORRADE_IGNORE_DEPRECATED_PUSH /* MSVC warns here */
 MeshData2D::MeshData2D(MeshData2D&&)
     #if !defined(__GNUC__) || __GNUC__*100 + __GNUC_MINOR__ != 409
     noexcept
     #endif
     = default;
+CORRADE_IGNORE_DEPRECATED_POP
 
 MeshData2D::~MeshData2D() = default;
 
+CORRADE_IGNORE_DEPRECATED_PUSH /* GCC why you warn on return and not on param */
 MeshData2D& MeshData2D::operator=(MeshData2D&&)
     #if !defined(__GNUC__) || __GNUC__*100 + __GNUC_MINOR__ != 409
     noexcept
     #endif
     = default;
+CORRADE_IGNORE_DEPRECATED_POP
 
 std::vector<UnsignedInt>& MeshData2D::indices() {
     CORRADE_ASSERT(isIndexed(), "Trade::MeshData2D::indices(): the mesh is not indexed", _indices);
diff --git a/src/Magnum/Trade/MeshData2D.h b/src/Magnum/Trade/MeshData2D.h
index 52170fa31..0bd12a8b8 100644
--- a/src/Magnum/Trade/MeshData2D.h
+++ b/src/Magnum/Trade/MeshData2D.h
@@ -25,14 +25,25 @@
     DEALINGS IN THE SOFTWARE.
 */
 
+#ifdef MAGNUM_BUILD_DEPRECATED
 /** @file
  * @brief Class @ref Magnum::Trade::MeshData2D
+ * @m_deprecated_since_latest Use @ref Magnum/Trade/MeshData.h and the
+ *      @ref Magnum::Trade::MeshData "MeshData" class instead.
  */
+#endif
+
+#include "Magnum/configure.h"
 
+#ifdef MAGNUM_BUILD_DEPRECATED
 #include <vector>
 
 #include "Magnum/Trade/MeshData.h"
 
+#ifndef _MAGNUM_NO_DEPRECATED_MESHDATA
+CORRADE_DEPRECATED_FILE("use Magnum/Trade/MeshData.h and the MeshData class instead")
+#endif
+
 namespace Magnum { namespace Trade {
 
 /**
@@ -48,9 +59,11 @@ directly to vertex positions:
 
 @snippet MagnumTrade.cpp MeshData2D-transform
 
+@m_deprecated_since_latest Use @ref MeshData instead.
+
 @see @ref AbstractImporter::mesh2D(), @ref MeshData3D
 */
-class MAGNUM_TRADE_EXPORT MeshData2D {
+class CORRADE_DEPRECATED("use MeshData instead") MAGNUM_TRADE_EXPORT MeshData2D {
     public:
         /**
          * @brief Constructor
@@ -181,5 +194,8 @@ class MAGNUM_TRADE_EXPORT MeshData2D {
 };
 
 }}
+#else
+#error use Magnum/Trade/MeshData.h and the MeshData class instead
+#endif
 
 #endif
diff --git a/src/Magnum/Trade/MeshData3D.cpp b/src/Magnum/Trade/MeshData3D.cpp
index edb21cd2a..a3e990ae4 100644
--- a/src/Magnum/Trade/MeshData3D.cpp
+++ b/src/Magnum/Trade/MeshData3D.cpp
@@ -23,6 +23,9 @@
     DEALINGS IN THE SOFTWARE.
 */
 
+/* There's no better way to disable file deprecation warnings */
+#define _MAGNUM_NO_DEPRECATED_MESHDATA
+
 #include "MeshData3D.h"
 
 #include <Corrade/Containers/ArrayViewStl.h>
@@ -69,19 +72,23 @@ MeshData3D::MeshData3D(const MeshData& other): _primitive{other.primitive()}, _i
 }
 #endif
 
+CORRADE_IGNORE_DEPRECATED_PUSH /* MSVC warns here */
 MeshData3D::MeshData3D(MeshData3D&&)
     #if !defined(__GNUC__) || __GNUC__*100 + __GNUC_MINOR__ != 409
     noexcept
     #endif
     = default;
+CORRADE_IGNORE_DEPRECATED_POP
 
 MeshData3D::~MeshData3D() = default;
 
+CORRADE_IGNORE_DEPRECATED_PUSH /* GCC why you warn on return and not on param */
 MeshData3D& MeshData3D::operator=(MeshData3D&&)
     #if !defined(__GNUC__) || __GNUC__*100 + __GNUC_MINOR__ != 409
     noexcept
     #endif
     = default;
+CORRADE_IGNORE_DEPRECATED_POP
 
 std::vector<UnsignedInt>& MeshData3D::indices() {
     CORRADE_ASSERT(isIndexed(), "Trade::MeshData3D::indices(): the mesh is not indexed", _indices);
diff --git a/src/Magnum/Trade/MeshData3D.h b/src/Magnum/Trade/MeshData3D.h
index c17416783..804ef8f38 100644
--- a/src/Magnum/Trade/MeshData3D.h
+++ b/src/Magnum/Trade/MeshData3D.h
@@ -25,14 +25,25 @@
     DEALINGS IN THE SOFTWARE.
 */
 
+#ifdef MAGNUM_BUILD_DEPRECATED
 /** @file
  * @brief Class @ref Magnum::Trade::MeshData3D
+ * @m_deprecated_since_latest Use @ref Magnum/Trade/MeshData.h and the
+ *      @ref Magnum::Trade::MeshData "MeshData" class instead.
  */
+#endif
+
+#include "Magnum/configure.h"
 
+#ifdef MAGNUM_BUILD_DEPRECATED
 #include <vector>
 
 #include "Magnum/Trade/MeshData.h"
 
+#ifndef _MAGNUM_NO_DEPRECATED_MESHDATA
+CORRADE_DEPRECATED_FILE("use Magnum/Trade/MeshData.h and the MeshData class instead")
+#endif
+
 namespace Magnum { namespace Trade {
 
 /**
@@ -48,9 +59,11 @@ to positions and normals:
 
 @snippet MagnumTrade.cpp MeshData3D-transform
 
+@m_deprecated_since_latest Use @ref MeshData instead.
+
 @see @ref AbstractImporter::mesh3D(), @ref MeshData2D
 */
-class MAGNUM_TRADE_EXPORT MeshData3D {
+class CORRADE_DEPRECATED("use MeshData instead") MAGNUM_TRADE_EXPORT MeshData3D {
     public:
         /**
          * @brief Constructor
@@ -198,5 +211,8 @@ class MAGNUM_TRADE_EXPORT MeshData3D {
 };
 
 }}
+#else
+#error use Magnum/Trade/MeshData.h and the MeshData class instead
+#endif
 
 #endif
diff --git a/src/Magnum/Trade/Test/AbstractImporterTest.cpp b/src/Magnum/Trade/Test/AbstractImporterTest.cpp
index 1f3a7c29d..1535abb05 100644
--- a/src/Magnum/Trade/Test/AbstractImporterTest.cpp
+++ b/src/Magnum/Trade/Test/AbstractImporterTest.cpp
@@ -46,6 +46,8 @@
 #include "Magnum/Trade/TextureData.h"
 
 #ifdef MAGNUM_BUILD_DEPRECATED
+#define _MAGNUM_NO_DEPRECATED_MESHDATA /* So it doesn't yell here */
+
 #include "Magnum/Trade/MeshData2D.h"
 #include "Magnum/Trade/MeshData3D.h"
 #endif
diff --git a/src/Magnum/Trade/Test/CMakeLists.txt b/src/Magnum/Trade/Test/CMakeLists.txt
index 2c9177347..f89f44e45 100644
--- a/src/Magnum/Trade/Test/CMakeLists.txt
+++ b/src/Magnum/Trade/Test/CMakeLists.txt
@@ -49,8 +49,6 @@ corrade_add_test(TradeImageDataTest ImageDataTest.cpp LIBRARIES MagnumTradeTestL
 corrade_add_test(TradeLightDataTest LightDataTest.cpp LIBRARIES MagnumTrade)
 corrade_add_test(TradeMaterialDataTest MaterialDataTest.cpp LIBRARIES MagnumTradeTestLib)
 corrade_add_test(TradeMeshDataTest MeshDataTest.cpp LIBRARIES MagnumTradeTestLib)
-corrade_add_test(TradeMeshData2DTest MeshData2DTest.cpp LIBRARIES MagnumTrade)
-corrade_add_test(TradeMeshData3DTest MeshData3DTest.cpp LIBRARIES MagnumTrade)
 corrade_add_test(TradeObjectData2DTest ObjectData2DTest.cpp LIBRARIES MagnumTradeTestLib)
 corrade_add_test(TradeObjectData3DTest ObjectData3DTest.cpp LIBRARIES MagnumTradeTestLib)
 corrade_add_test(TradeSceneDataTest SceneDataTest.cpp LIBRARIES MagnumTrade)
@@ -69,10 +67,18 @@ set_target_properties(
     TradeImageDataTest
     TradeLightDataTest
     TradeMaterialDataTest
-    TradeMeshData2DTest
-    TradeMeshData3DTest
     TradeObjectData2DTest
     TradeObjectData3DTest
     TradeSceneDataTest
     TradeTextureDataTest
     PROPERTIES FOLDER "Magnum/Trade/Test")
+
+if(MAGNUM_BUILD_DEPRECATED)
+    corrade_add_test(TradeMeshData2DTest MeshData2DTest.cpp LIBRARIES MagnumTrade)
+    corrade_add_test(TradeMeshData3DTest MeshData3DTest.cpp LIBRARIES MagnumTrade)
+
+    set_target_properties(
+        TradeMeshData2DTest
+        TradeMeshData3DTest
+        PROPERTIES FOLDER "Magnum/Trade/Test")
+endif()
diff --git a/src/Magnum/Trade/Test/MeshData2DTest.cpp b/src/Magnum/Trade/Test/MeshData2DTest.cpp
index 34a38b0c8..dc1def1c7 100644
--- a/src/Magnum/Trade/Test/MeshData2DTest.cpp
+++ b/src/Magnum/Trade/Test/MeshData2DTest.cpp
@@ -23,6 +23,9 @@
     DEALINGS IN THE SOFTWARE.
 */
 
+/* There's no better way to disable file deprecation warnings */
+#define _MAGNUM_NO_DEPRECATED_MESHDATA
+
 #include <Corrade/TestSuite/Tester.h>
 
 #include "Magnum/Mesh.h"
@@ -42,6 +45,8 @@ struct MeshData2DTest: TestSuite::Tester {
     void constructMove();
 };
 
+CORRADE_IGNORE_DEPRECATED_PUSH
+
 using namespace Math::Literals;
 
 const UnsignedByte Indices[]{12, 1, 0};
@@ -59,7 +64,6 @@ const struct Vertex {
 };
 const int State = 3;
 
-CORRADE_IGNORE_DEPRECATED_PUSH
 struct {
     const char* name;
     const MeshData2D data, dataNonIndexed;
@@ -103,7 +107,6 @@ struct {
             },  &State}
     }
 };
-CORRADE_IGNORE_DEPRECATED_POP
 
 MeshData2DTest::MeshData2DTest() {
     addInstancedTests({&MeshData2DTest::construct,
@@ -220,6 +223,8 @@ void MeshData2DTest::constructMove() {
     CORRADE_COMPARE(d.importerState(), &a);
 }
 
+CORRADE_IGNORE_DEPRECATED_POP
+
 }}}}
 
 CORRADE_TEST_MAIN(Magnum::Trade::Test::MeshData2DTest)
diff --git a/src/Magnum/Trade/Test/MeshData3DTest.cpp b/src/Magnum/Trade/Test/MeshData3DTest.cpp
index 1244120ad..e7ab2dd11 100644
--- a/src/Magnum/Trade/Test/MeshData3DTest.cpp
+++ b/src/Magnum/Trade/Test/MeshData3DTest.cpp
@@ -23,6 +23,9 @@
     DEALINGS IN THE SOFTWARE.
 */
 
+/* There's no better way to disable file deprecation warnings */
+#define _MAGNUM_NO_DEPRECATED_MESHDATA
+
 #include <Corrade/TestSuite/Tester.h>
 
 #include "Magnum/Mesh.h"
@@ -43,6 +46,8 @@ struct MeshData3DTest: TestSuite::Tester {
     void constructMove();
 };
 
+CORRADE_IGNORE_DEPRECATED_PUSH
+
 using namespace Math::Literals;
 
 const UnsignedByte Indices[]{12, 1, 0};
@@ -63,7 +68,6 @@ const struct Vertex {
 };
 const int State = 3;
 
-CORRADE_IGNORE_DEPRECATED_PUSH
 struct {
     const char* name;
     const MeshData3D data, dataNonIndexed;
@@ -113,7 +117,6 @@ struct {
             },  &State}
     }
 };
-CORRADE_IGNORE_DEPRECATED_POP
 
 MeshData3DTest::MeshData3DTest() {
     addInstancedTests({&MeshData3DTest::construct,
@@ -254,6 +257,8 @@ void MeshData3DTest::constructMove() {
     CORRADE_COMPARE(d.importerState(), &a);
 }
 
+CORRADE_IGNORE_DEPRECATED_POP
+
 }}}}
 
 CORRADE_TEST_MAIN(Magnum::Trade::Test::MeshData3DTest)
diff --git a/src/Magnum/Trade/Trade.h b/src/Magnum/Trade/Trade.h
index 36c16f70b..d4df385bd 100644
--- a/src/Magnum/Trade/Trade.h
+++ b/src/Magnum/Trade/Trade.h
@@ -74,8 +74,10 @@ class MeshIndexData;
 class MeshAttributeData;
 class MeshData;
 
-class MeshData2D;
-class MeshData3D;
+#ifdef MAGNUM_BUILD_DEPRECATED
+class CORRADE_DEPRECATED("use MeshData instead") MeshData2D;
+class CORRADE_DEPRECATED("use MeshData instead") MeshData3D;
+#endif
 class MeshObjectData2D;
 class MeshObjectData3D;
 class ObjectData2D;