diff --git a/src/MagnumPlugins/AnySceneImporter/AnySceneImporter.cpp b/src/MagnumPlugins/AnySceneImporter/AnySceneImporter.cpp
index 18c86b14a..0e7faa2b7 100644
--- a/src/MagnumPlugins/AnySceneImporter/AnySceneImporter.cpp
+++ b/src/MagnumPlugins/AnySceneImporter/AnySceneImporter.cpp
@@ -36,13 +36,19 @@
 #include "Magnum/Trade/CameraData.h"
 #include "Magnum/Trade/ImageData.h"
 #include "Magnum/Trade/LightData.h"
-#include "Magnum/Trade/MeshData2D.h"
-#include "Magnum/Trade/MeshData3D.h"
+#include "Magnum/Trade/MeshData.h"
 #include "Magnum/Trade/ObjectData2D.h"
 #include "Magnum/Trade/ObjectData3D.h"
 #include "Magnum/Trade/SceneData.h"
 #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
+
 namespace Magnum { namespace Trade {
 
 AnySceneImporter::AnySceneImporter(PluginManager::Manager<AbstractImporter>& manager): AbstractImporter{manager} {}
@@ -175,6 +181,16 @@ Int AnySceneImporter::doObject3DForName(const std::string& name) { return _in->o
 std::string AnySceneImporter::doObject3DName(const UnsignedInt id) { return _in->object3DName(id); }
 Containers::Pointer<ObjectData3D> AnySceneImporter::doObject3D(const UnsignedInt id) { return _in->object3D(id); }
 
+UnsignedInt AnySceneImporter::doMeshCount() const { return _in->meshCount(); }
+Int AnySceneImporter::doMeshForName(const std::string& name) { return _in->meshForName(name); }
+std::string AnySceneImporter::doMeshName(const UnsignedInt id) { return _in->meshName(id); }
+Containers::Optional<MeshData> AnySceneImporter::doMesh(const UnsignedInt id, const UnsignedInt level) { return _in->mesh(id, level); }
+
+MeshAttribute AnySceneImporter::doMeshAttributeForName(const std::string& name) { return _in->meshAttributeForName(name); }
+std::string AnySceneImporter::doMeshAttributeName(const UnsignedShort id) { return _in->meshAttributeName(meshAttributeCustom(id)); }
+
+#ifdef MAGNUM_BUILD_DEPRECATED
+CORRADE_IGNORE_DEPRECATED_PUSH
 UnsignedInt AnySceneImporter::doMesh2DCount() const { return _in->mesh2DCount(); }
 Int AnySceneImporter::doMesh2DForName(const std::string& name) { return _in->mesh2DForName(name); }
 std::string AnySceneImporter::doMesh2DName(const UnsignedInt id) { return _in->mesh2DName(id); }
@@ -184,6 +200,8 @@ UnsignedInt AnySceneImporter::doMesh3DCount() const { return _in->mesh3DCount();
 Int AnySceneImporter::doMesh3DForName(const std::string& name) { return _in->mesh3DForName(name); }
 std::string AnySceneImporter::doMesh3DName(const UnsignedInt id) { return _in->mesh3DName(id); }
 Containers::Optional<MeshData3D> AnySceneImporter::doMesh3D(const UnsignedInt id) { return _in->mesh3D(id); }
+CORRADE_IGNORE_DEPRECATED_POP
+#endif
 
 UnsignedInt AnySceneImporter::doMaterialCount() const { return _in->materialCount(); }
 Int AnySceneImporter::doMaterialForName(const std::string& name) { return _in->materialForName(name); }
diff --git a/src/MagnumPlugins/AnySceneImporter/AnySceneImporter.h b/src/MagnumPlugins/AnySceneImporter/AnySceneImporter.h
index 1cb4868b0..743bd86a4 100644
--- a/src/MagnumPlugins/AnySceneImporter/AnySceneImporter.h
+++ b/src/MagnumPlugins/AnySceneImporter/AnySceneImporter.h
@@ -175,15 +175,29 @@ class MAGNUM_ANYSCENEIMPORTER_EXPORT AnySceneImporter: public AbstractImporter {
         MAGNUM_ANYSCENEIMPORTER_LOCAL std::string doObject3DName(UnsignedInt id) override;
         MAGNUM_ANYSCENEIMPORTER_LOCAL Containers::Pointer<ObjectData3D> doObject3D(UnsignedInt id) override;
 
+        MAGNUM_ANYSCENEIMPORTER_LOCAL UnsignedInt doMeshCount() const override;
+        MAGNUM_ANYSCENEIMPORTER_LOCAL Int doMeshForName(const std::string& name) override;
+        MAGNUM_ANYSCENEIMPORTER_LOCAL std::string doMeshName(UnsignedInt id) override;
+        MAGNUM_ANYSCENEIMPORTER_LOCAL Containers::Optional<MeshData> doMesh(UnsignedInt id, UnsignedInt level) override;
+
+        MAGNUM_ANYSCENEIMPORTER_LOCAL MeshAttribute doMeshAttributeForName(const std::string& name) override;
+        MAGNUM_ANYSCENEIMPORTER_LOCAL std::string doMeshAttributeName(UnsignedShort id) override;
+
+        #ifdef MAGNUM_BUILD_DEPRECATED
         MAGNUM_ANYSCENEIMPORTER_LOCAL UnsignedInt doMesh2DCount() const override;
         MAGNUM_ANYSCENEIMPORTER_LOCAL Int doMesh2DForName(const std::string& name) override;
         MAGNUM_ANYSCENEIMPORTER_LOCAL std::string doMesh2DName(UnsignedInt id) override;
+        CORRADE_IGNORE_DEPRECATED_PUSH
         MAGNUM_ANYSCENEIMPORTER_LOCAL Containers::Optional<MeshData2D> doMesh2D(UnsignedInt id) override;
+        CORRADE_IGNORE_DEPRECATED_POP
 
         MAGNUM_ANYSCENEIMPORTER_LOCAL UnsignedInt doMesh3DCount() const override;
         MAGNUM_ANYSCENEIMPORTER_LOCAL Int doMesh3DForName(const std::string& name) override;
         MAGNUM_ANYSCENEIMPORTER_LOCAL std::string doMesh3DName(UnsignedInt id) override;
+        CORRADE_IGNORE_DEPRECATED_PUSH
         MAGNUM_ANYSCENEIMPORTER_LOCAL Containers::Optional<MeshData3D> doMesh3D(UnsignedInt id) override;
+        CORRADE_IGNORE_DEPRECATED_POP
+        #endif
 
         MAGNUM_ANYSCENEIMPORTER_LOCAL UnsignedInt doMaterialCount() const override;
         MAGNUM_ANYSCENEIMPORTER_LOCAL Int doMaterialForName(const std::string& name) override;
diff --git a/src/MagnumPlugins/AnySceneImporter/Test/AnySceneImporterTest.cpp b/src/MagnumPlugins/AnySceneImporter/Test/AnySceneImporterTest.cpp
index 325f4cf2b..722754bb9 100644
--- a/src/MagnumPlugins/AnySceneImporter/Test/AnySceneImporterTest.cpp
+++ b/src/MagnumPlugins/AnySceneImporter/Test/AnySceneImporterTest.cpp
@@ -33,7 +33,13 @@
 
 #include "Magnum/Math/Vector3.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/MeshData3D.h"
+#endif
 
 #include "configure.h"
 
@@ -43,6 +49,9 @@ struct AnySceneImporterTest: TestSuite::Tester {
     explicit AnySceneImporterTest();
 
     void load();
+    #ifdef MAGNUM_BUILD_DEPRECATED
+    void loadDeprecatedMeshData();
+    #endif
     void detect();
 
     void unknown();
@@ -79,6 +88,10 @@ AnySceneImporterTest::AnySceneImporterTest() {
     addInstancedTests({&AnySceneImporterTest::load},
         Containers::arraySize(LoadData));
 
+    #ifdef MAGNUM_BUILD_DEPRECATED
+    addTests({&AnySceneImporterTest::loadDeprecatedMeshData});
+    #endif
+
     addInstancedTests({&AnySceneImporterTest::detect},
         Containers::arraySize(DetectData));
 
@@ -106,13 +119,35 @@ void AnySceneImporterTest::load() {
     CORRADE_VERIFY(importer->openFile(data.filename));
 
     /* Check only size, as it is good enough proof that it is working */
+    Containers::Optional<MeshData> mesh = importer->mesh(0);
+    CORRADE_VERIFY(mesh);
+    CORRADE_COMPARE(mesh->vertexCount(), 3);
+
+    importer->close();
+    CORRADE_VERIFY(!importer->isOpened());
+}
+
+#ifdef MAGNUM_BUILD_DEPRECATED
+void AnySceneImporterTest::loadDeprecatedMeshData() {
+    if(!(_manager.loadState("ObjImporter") & PluginManager::LoadState::Loaded))
+        CORRADE_SKIP("ObjImporter plugin not enabled, cannot test");
+
+    Containers::Pointer<AbstractImporter> importer = _manager.instantiate("AnySceneImporter");
+    CORRADE_VERIFY(importer->openFile(OBJ_FILE));
+
+    /* Check only size, as it is good enough proof that it is working */
+
+    /* MSVC warns also on positions() */
+    CORRADE_IGNORE_DEPRECATED_PUSH
     Containers::Optional<MeshData3D> mesh = importer->mesh3D(0);
     CORRADE_VERIFY(mesh);
     CORRADE_COMPARE(mesh->positions(0).size(), 3);
+    CORRADE_IGNORE_DEPRECATED_POP
 
     importer->close();
     CORRADE_VERIFY(!importer->isOpened());
 }
+#endif
 
 void AnySceneImporterTest::detect() {
     auto&& data = DetectData[testCaseInstanceId()];