diff --git a/doc/changelog.dox b/doc/changelog.dox
index 7fd25d432..c0843866f 100644
--- a/doc/changelog.dox
+++ b/doc/changelog.dox
@@ -1279,6 +1279,10 @@ See also:
     @ref Math::RectangularMatrix::data() are no longer @cpp constexpr @ce in
     order to make them return a reference to a fixed-size array instead of a
     pointer, which was deemed a more useful property.
+-   @ref MeshTools::primitiveCount() now requires the element count to follow
+    rules defined by a particular primitive to be consistent with requirements
+    of @ref MeshTools::generateIndices() and related APIs. Before it was just
+    rounding down to the nearest lower primitive count.
 -   @cpp Platform::WindowlessWindowsEglApplication @ce is now merged into
     @ref Platform::WindowlessEglApplication. Since its use case was rather rare
     (windowless applications on ANGLE on Windows) and it wasn't even built in
diff --git a/src/Magnum/MeshTools/GenerateIndices.cpp b/src/Magnum/MeshTools/GenerateIndices.cpp
index 1422ca359..d6d61323a 100644
--- a/src/Magnum/MeshTools/GenerateIndices.cpp
+++ b/src/Magnum/MeshTools/GenerateIndices.cpp
@@ -36,6 +36,32 @@
 namespace Magnum { namespace MeshTools {
 
 UnsignedInt primitiveCount(const MeshPrimitive primitive, const UnsignedInt elementCount) {
+    #ifndef CORRADE_NO_ASSERT
+    UnsignedInt minElementCount;
+    if(primitive == MeshPrimitive::Lines ||
+       primitive == MeshPrimitive::LineStrip ||
+       primitive == MeshPrimitive::LineLoop)
+        minElementCount = 2;
+    else if(primitive == MeshPrimitive::Triangles ||
+            primitive == MeshPrimitive::TriangleStrip ||
+            primitive == MeshPrimitive::TriangleFan)
+        minElementCount = 3;
+    else
+        minElementCount = 1;
+    CORRADE_ASSERT(elementCount == 0 || elementCount >= minElementCount,
+        "MeshTools::primitiveCount(): expected either zero or at least" << minElementCount << "elements for" << primitive << Debug::nospace << ", got" << elementCount, {});
+
+    UnsignedInt elementCountDivisor;
+    if(primitive == MeshPrimitive::Lines)
+        elementCountDivisor = 2;
+    else if(primitive == MeshPrimitive::Triangles)
+        elementCountDivisor = 3;
+    else
+        elementCountDivisor = 1;
+    CORRADE_ASSERT(elementCount % elementCountDivisor == 0,
+        "MeshTools::primitiveCount(): expected element count to be divisible by" << elementCountDivisor << "for" << primitive << Debug::nospace << ", got" << elementCount, {});
+    #endif
+
     if(primitive == MeshPrimitive::Points ||
        primitive == MeshPrimitive::Edges ||
        primitive == MeshPrimitive::Faces ||
diff --git a/src/Magnum/MeshTools/GenerateIndices.h b/src/Magnum/MeshTools/GenerateIndices.h
index dbcd2532e..6e8c49436 100644
--- a/src/Magnum/MeshTools/GenerateIndices.h
+++ b/src/Magnum/MeshTools/GenerateIndices.h
@@ -42,9 +42,10 @@ namespace Magnum { namespace MeshTools {
 
 Returns how many primitives is generated for given @p primitive and
 @p elementCount, for example for @ref MeshPrimitive::Triangles returns
-@cpp elementCount/3 @ce. Expects that @p primitive is valid, return value is
-rounded down if there's not enough elements for given primitive type (so for
-14 vertices you get just 4 triangles, for example).
+@cpp elementCount/3 @ce. Expects that @p primitive is valid, @p elementCount
+is either zero or at least @cpp 2 @ce for a line-based primitive and at least
+@cpp 3 @ce for a triangle-based primitive, is divisible by @cpp 2 @ce for
+@ref MeshPrimitive::Lines and by @cpp 3 @ce for @ref MeshPrimitive::Triangles.
 */
 MAGNUM_MESHTOOLS_EXPORT UnsignedInt primitiveCount(MeshPrimitive primitive, UnsignedInt elementCount);
 
diff --git a/src/Magnum/MeshTools/Test/GenerateIndicesTest.cpp b/src/Magnum/MeshTools/Test/GenerateIndicesTest.cpp
index c003a4da6..ca8087881 100644
--- a/src/Magnum/MeshTools/Test/GenerateIndicesTest.cpp
+++ b/src/Magnum/MeshTools/Test/GenerateIndicesTest.cpp
@@ -42,6 +42,7 @@ struct GenerateIndicesTest: TestSuite::Tester {
     explicit GenerateIndicesTest();
 
     void primitiveCount();
+    void primitiveCountInvalidVertexCount();
     void primitiveCountInvalidPrimitive();
 
     void generateLineStripIndices();
@@ -175,6 +176,7 @@ const struct {
 
 GenerateIndicesTest::GenerateIndicesTest() {
     addTests({&GenerateIndicesTest::primitiveCount,
+              &GenerateIndicesTest::primitiveCountInvalidVertexCount,
               &GenerateIndicesTest::primitiveCountInvalidPrimitive,
 
               &GenerateIndicesTest::generateLineStripIndices,
@@ -224,26 +226,43 @@ void GenerateIndicesTest::primitiveCount() {
     CORRADE_COMPARE(MeshTools::primitiveCount(MeshPrimitive::Instances, 13), 13);
 
     CORRADE_COMPARE(MeshTools::primitiveCount(MeshPrimitive::Lines, 4), 2);
-    CORRADE_COMPARE(MeshTools::primitiveCount(MeshPrimitive::Lines, 5), 2);
+    CORRADE_COMPARE(MeshTools::primitiveCount(MeshPrimitive::Lines, 14), 7);
 
-    CORRADE_COMPARE(MeshTools::primitiveCount(MeshPrimitive::LineStrip, 1), 0);
     CORRADE_COMPARE(MeshTools::primitiveCount(MeshPrimitive::LineStrip, 2), 1);
     CORRADE_COMPARE(MeshTools::primitiveCount(MeshPrimitive::LineStrip, 4), 3);
+    CORRADE_COMPARE(MeshTools::primitiveCount(MeshPrimitive::LineStrip, 10), 9);
 
-    /* This is a degenerate line, which technically still is a primitive */
-    CORRADE_COMPARE(MeshTools::primitiveCount(MeshPrimitive::LineLoop, 1), 1);
     CORRADE_COMPARE(MeshTools::primitiveCount(MeshPrimitive::LineLoop, 2), 2);
+    CORRADE_COMPARE(MeshTools::primitiveCount(MeshPrimitive::LineLoop, 9), 9);
 
-    CORRADE_COMPARE(MeshTools::primitiveCount(MeshPrimitive::Triangles, 2), 0);
     CORRADE_COMPARE(MeshTools::primitiveCount(MeshPrimitive::Triangles, 3), 1);
     CORRADE_COMPARE(MeshTools::primitiveCount(MeshPrimitive::Triangles, 6), 2);
+    CORRADE_COMPARE(MeshTools::primitiveCount(MeshPrimitive::Triangles, 21), 7);
 
-    CORRADE_COMPARE(MeshTools::primitiveCount(MeshPrimitive::TriangleStrip, 2), 0);
-    CORRADE_COMPARE(MeshTools::primitiveCount(MeshPrimitive::TriangleFan, 2), 0);
     CORRADE_COMPARE(MeshTools::primitiveCount(MeshPrimitive::TriangleStrip, 3), 1);
     CORRADE_COMPARE(MeshTools::primitiveCount(MeshPrimitive::TriangleFan, 3), 1);
     CORRADE_COMPARE(MeshTools::primitiveCount(MeshPrimitive::TriangleStrip, 7), 5);
     CORRADE_COMPARE(MeshTools::primitiveCount(MeshPrimitive::TriangleFan, 7), 5);
+    CORRADE_COMPARE(MeshTools::primitiveCount(MeshPrimitive::TriangleStrip, 22), 20);
+    CORRADE_COMPARE(MeshTools::primitiveCount(MeshPrimitive::TriangleFan, 22), 20);
+}
+
+void GenerateIndicesTest::primitiveCountInvalidVertexCount() {
+    CORRADE_SKIP_IF_NO_ASSERT();
+
+    std::ostringstream out;
+    Error redirectError{&out};
+    MeshTools::primitiveCount(MeshPrimitive::LineLoop, 1);
+    MeshTools::primitiveCount(MeshPrimitive::TriangleStrip, 1);
+    MeshTools::primitiveCount(MeshPrimitive::TriangleFan, 2);
+    MeshTools::primitiveCount(MeshPrimitive::Lines, 7);
+    MeshTools::primitiveCount(MeshPrimitive::Triangles, 14);
+    CORRADE_COMPARE(out.str(),
+        "MeshTools::primitiveCount(): expected either zero or at least 2 elements for MeshPrimitive::LineLoop, got 1\n"
+        "MeshTools::primitiveCount(): expected either zero or at least 3 elements for MeshPrimitive::TriangleStrip, got 1\n"
+        "MeshTools::primitiveCount(): expected either zero or at least 3 elements for MeshPrimitive::TriangleFan, got 2\n"
+        "MeshTools::primitiveCount(): expected element count to be divisible by 2 for MeshPrimitive::Lines, got 7\n"
+        "MeshTools::primitiveCount(): expected element count to be divisible by 3 for MeshPrimitive::Triangles, got 14\n");
 }
 
 void GenerateIndicesTest::primitiveCountInvalidPrimitive() {