diff --git a/src/Magnum/MeshTools/CompressIndices.cpp b/src/Magnum/MeshTools/CompressIndices.cpp
index 09c1fb398..9ad23b7c3 100644
--- a/src/Magnum/MeshTools/CompressIndices.cpp
+++ b/src/Magnum/MeshTools/CompressIndices.cpp
@@ -51,6 +51,10 @@ template<class T, class U> inline Containers::Array<char> compress(const Contain
 }
 
 template<class T> std::pair<Containers::Array<char>, MeshIndexType> compressIndicesImplementation(const Containers::StridedArrayView1D<const T>& indices, const MeshIndexType atLeast, const Long offset) {
+    CORRADE_ASSERT(!isMeshIndexTypeImplementationSpecific(atLeast),
+        "MeshTools::compressIndices(): can't compress to an implementation-specific index type" << reinterpret_cast<void*>(meshIndexTypeUnwrap(atLeast)),
+        (std::pair<Containers::Array<char>, MeshIndexType>{nullptr, MeshIndexType::UnsignedInt}));
+
     const UnsignedInt max = Math::max(indices) - offset;
     Containers::Array<char> out;
     MeshIndexType type;
@@ -144,6 +148,9 @@ Trade::MeshData compressIndices(Trade::MeshData&& data, MeshIndexType atLeast) {
         offset = Math::min(indices);
         result = compressIndicesImplementation<UnsignedShort>(indices, atLeast, offset);
     } else {
+        CORRADE_ASSERT(!isMeshIndexTypeImplementationSpecific(data.indexType()),
+            "MeshTools::compressIndices(): mesh has an implementation-specific index type" << reinterpret_cast<void*>(meshIndexTypeUnwrap(data.indexType())),
+            (Trade::MeshData{MeshPrimitive{}, 0}));
         CORRADE_INTERNAL_ASSERT(data.indexType() == MeshIndexType::UnsignedByte);
         auto indices = data.indices<UnsignedByte>();
         offset = Math::min(indices);
@@ -163,7 +170,7 @@ Trade::MeshData compressIndices(Trade::MeshData&& data, MeshIndexType atLeast) {
 
     Trade::MeshIndexData indices{result.second, result.first};
     return Trade::MeshData{data.primitive(), std::move(result.first), indices,
-        std::move(vertexData), std::move(attributeData)};
+        std::move(vertexData), std::move(attributeData), newVertexCount};
 }
 
 Trade::MeshData compressIndices(const Trade::MeshData& data, MeshIndexType atLeast) {
diff --git a/src/Magnum/MeshTools/CompressIndices.h b/src/Magnum/MeshTools/CompressIndices.h
index c7bab3cdf..ceffa2d48 100644
--- a/src/Magnum/MeshTools/CompressIndices.h
+++ b/src/Magnum/MeshTools/CompressIndices.h
@@ -75,6 +75,9 @@ offsets accordingly. Example:
 A negative @p offset value will do an operation inverse to the above. See also
 @ref compressIndices(const Trade::MeshData&, MeshIndexType) that can do this
 operation directly on a @ref Trade::MeshData instance.
+
+The @p atLeast parameter is expected to not be an implementation-specific type.
+@see @ref isMeshIndexTypeImplementationSpecific()
 */
 MAGNUM_MESHTOOLS_EXPORT std::pair<Containers::Array<char>, MeshIndexType> compressIndices(const Containers::StridedArrayView1D<const UnsignedInt>& indices, MeshIndexType atLeast = MeshIndexType::UnsignedShort, Long offset = 0);
 
@@ -125,6 +128,9 @@ Expects that the second dimension of @p indices is contiguous and represents
 the actual 1/2/4-byte index type. Based on its size then calls one of the
 @ref compressIndices(const Containers::StridedArrayView1D<const UnsignedInt>&, MeshIndexType, Long)
 etc. overloads.
+
+The @p atLeast parameter is expected to not be an implementation-specific type.
+@see @ref isMeshIndexTypeImplementationSpecific()
 */
 MAGNUM_MESHTOOLS_EXPORT std::pair<Containers::Array<char>, MeshIndexType> compressIndices(const Containers::StridedArrayView2D<const char>& indices, MeshIndexType atLeast = MeshIndexType::UnsignedShort, Long offset = 0);
 
@@ -146,6 +152,10 @@ but together with adjusting vertex attribute offsets in the passed
 @ref Trade::MeshData instance. This function will unconditionally make a copy
 of all vertex data, use @ref compressIndices(Trade::MeshData&&, MeshIndexType)
 to avoid that copy.
+
+The mesh is expected to be indexed and the index type and the @p atLeast
+parameter is expected to not be implementation-specific type.
+@see @ref isMeshIndexTypeImplementationSpecific()
 */
 MAGNUM_MESHTOOLS_EXPORT Trade::MeshData compressIndices(const Trade::MeshData& data, MeshIndexType atLeast = MeshIndexType::UnsignedShort);
 
diff --git a/src/Magnum/MeshTools/Test/CompressIndicesTest.cpp b/src/Magnum/MeshTools/Test/CompressIndicesTest.cpp
index 56332395f..e849e8429 100644
--- a/src/Magnum/MeshTools/Test/CompressIndicesTest.cpp
+++ b/src/Magnum/MeshTools/Test/CompressIndicesTest.cpp
@@ -60,6 +60,8 @@ struct CompressIndicesTest: TestSuite::Tester {
     template<class T> void compressMeshData();
     void compressMeshDataMove();
     void compressMeshDataNonIndexed();
+    void compressMeshDataImplementationSpecificIndexType();
+    void compressMeshDataImplementationSpecificAtLeastIndexType();
 
     #ifdef MAGNUM_BUILD_DEPRECATED
     void compressAsShort();
@@ -89,6 +91,8 @@ CompressIndicesTest::CompressIndicesTest() {
               &CompressIndicesTest::compressMeshData<UnsignedInt>,
               &CompressIndicesTest::compressMeshDataMove,
               &CompressIndicesTest::compressMeshDataNonIndexed,
+              &CompressIndicesTest::compressMeshDataImplementationSpecificIndexType,
+              &CompressIndicesTest::compressMeshDataImplementationSpecificAtLeastIndexType,
 
               #ifdef MAGNUM_BUILD_DEPRECATED
               &CompressIndicesTest::compressAsShort
@@ -354,6 +358,40 @@ void CompressIndicesTest::compressMeshDataNonIndexed() {
         "MeshTools::compressIndices(): mesh data not indexed\n");
 }
 
+void CompressIndicesTest::compressMeshDataImplementationSpecificIndexType() {
+    #ifdef CORRADE_NO_ASSERT
+    CORRADE_SKIP("CORRADE_NO_ASSERT defined, can't test assertions");
+    #endif
+
+    Trade::MeshData mesh{MeshPrimitive::Points,
+        nullptr, Trade::MeshIndexData{meshIndexTypeWrap(0xcaca), Containers::StridedArrayView1D<const void>{}}, 1};
+
+    /* Test both r-value and l-value overload */
+    std::ostringstream out;
+    Error redirectError{&out};
+    MeshTools::compressIndices(mesh);
+    MeshTools::compressIndices(std::move(mesh));
+    CORRADE_COMPARE(out.str(),
+        "MeshTools::compressIndices(): mesh has an implementation-specific index type 0xcaca\n"
+        "MeshTools::compressIndices(): mesh has an implementation-specific index type 0xcaca\n");
+}
+
+void CompressIndicesTest::compressMeshDataImplementationSpecificAtLeastIndexType() {
+    #ifdef CORRADE_NO_ASSERT
+    CORRADE_SKIP("CORRADE_NO_ASSERT defined, can't test assertions");
+    #endif
+
+    UnsignedInt indices[5]{};
+    Trade::MeshData mesh{MeshPrimitive::Points,
+        {}, indices, Trade::MeshIndexData{indices}, 1};
+
+    std::ostringstream out;
+    Error redirectError{&out};
+    MeshTools::compressIndices(mesh, meshIndexTypeWrap(0xcaca));
+    CORRADE_COMPARE(out.str(),
+        "MeshTools::compressIndices(): can't compress to an implementation-specific index type 0xcaca\n");
+}
+
 #ifdef MAGNUM_BUILD_DEPRECATED
 void CompressIndicesTest::compressAsShort() {
     #ifdef CORRADE_NO_ASSERT