diff --git a/src/MagnumPlugins/AnySceneImporter/AnySceneImporter.cpp b/src/MagnumPlugins/AnySceneImporter/AnySceneImporter.cpp
index 5850ad472..62c7420e6 100644
--- a/src/MagnumPlugins/AnySceneImporter/AnySceneImporter.cpp
+++ b/src/MagnumPlugins/AnySceneImporter/AnySceneImporter.cpp
@@ -81,6 +81,34 @@ void AnySceneImporter::doOpenFile(const Containers::StringView filename) {
        extensions as well. But we can lowercase just the filename, at least. */
     const Containers::String normalized = Utility::String::lowercase(Utility::Path::filename(filename));
 
+    /* Some extensions supported by AssimpImporter are deliberately not
+       recognized due to being overly generic, conflicting, or too obscure. In particular:
+
+        -   `*.mdl`, used by both Quake I and "3D GameStudio (3DGS)"
+        -   `*.md2`, `*.md3`, `*.pk3`, `*.md5*` used by Quake II and III and
+            Doom 3, not recognized because Quake I isn't recognized either
+        -   `*.mesh`, which is OGRE, Meshwork and likely other formats too
+            http://justsolve.archiveteam.org/wiki/Meshwork_model
+            https://file.org/extension/mesh
+        -   `*.nff`, which is both "Neutral File Format" and
+            "Sense8 WorldToolKit"
+        -   `*.off`, which is "Object File Format", likely a variant of the
+            above, feels rather obscure
+        -   `*.ndo`, which is "Izware Nendo", feels rather obscure
+        -   `*.raw`, which can be PovRAY Raw, but also raw image data or just
+            anything. Especially problematic when e.g. magnum-player first
+            tries to open a file as a scene and if that fails, falls back to
+            opening an image.
+        -   `*.xml`, which can be an OGRE XML mesh but also COLLADA. Ogre XML
+            is recognized as `*.mesh.xml` instead.
+        -   `*.ter`, which is Terragen Terrain. I couldn't find any file that
+            would load with Assimp, the only `terrain.ter` I found is an
+            OBJ-like text file for which Assimp complains that "Magic string
+            'TERRAGEN' not found".
+
+       The conflicting extensions are explicitly tested in AnySceneImporterTest
+       to ensure they're not added by accident. */
+
     /* Detect the plugin from extension */
     Containers::StringView plugin;
     if(normalized.hasSuffix(".3ds"_s) ||
@@ -135,6 +163,7 @@ void AnySceneImporter::doOpenFile(const Containers::StringView filename) {
     else if(normalized.hasSuffix(".stl"_s))
         plugin = "StlImporter"_s;
     else if(normalized.hasSuffix(".cob"_s) ||
+            /** @todo isn't *.scn also too generic? */
             normalized.hasSuffix(".scn"_s))
         plugin = "TrueSpaceImporter"_s;
     else if(normalized.hasSuffix(".3d"_s))
diff --git a/src/MagnumPlugins/AnySceneImporter/AnySceneImporter.h b/src/MagnumPlugins/AnySceneImporter/AnySceneImporter.h
index 2a7a8c9e7..739dd7988 100644
--- a/src/MagnumPlugins/AnySceneImporter/AnySceneImporter.h
+++ b/src/MagnumPlugins/AnySceneImporter/AnySceneImporter.h
@@ -85,7 +85,9 @@ tries to open the file with it. Supported formats:
 -   Wavefront OBJ (`*.obj`), loaded with @ref ObjImporter or any other plugin
     that provides it
 -   OGRE XML (`*.mesh.xml`), loaded with any plugin that provides
-    `OgreImporter`
+    `OgreImporter`. The `*.mesh` extension isn't recognized because it's used
+    by [Meshwork](http://justsolve.archiveteam.org/wiki/Meshwork_model) as
+    well.
 -   OpenGEX (`*.ogex`), loaded with @ref OpenGexImporter or any other plugin
     that provides it
 -   Stanford (`*.ply`), loaded with @ref StanfordImporter or any other plugin
@@ -99,6 +101,14 @@ tries to open the file with it. Supported formats:
     `ValveImporter`
 -   XGL (`*.xgl`, `*.zgl`), loaded with any plugin that provides `XglImporter`
 
+@note
+    Note that this list is not exhaustive, in particular the
+    @ref AssimpImporter lists many more file extensions. Not all can be
+    supported by this plugin because they're either very generic or used by
+    multiple different formats, such as `*.mdl` used for both Quake I and 3D
+    GameStudio. If file opening fails with this plugin, you can try directly
+    with a concrete plugin such as the @ref AssimpImporter as a fallback.
+
 Only loading from files is supported as the filename is used to detect the
 format, however @ref ImporterFeature::FileCallback is supported as well.
 
diff --git a/src/MagnumPlugins/AnySceneImporter/Test/AnySceneImporterTest.cpp b/src/MagnumPlugins/AnySceneImporter/Test/AnySceneImporterTest.cpp
index 18e64916d..50fd26d9f 100644
--- a/src/MagnumPlugins/AnySceneImporter/Test/AnySceneImporterTest.cpp
+++ b/src/MagnumPlugins/AnySceneImporter/Test/AnySceneImporterTest.cpp
@@ -65,6 +65,7 @@ struct AnySceneImporterTest: TestSuite::Tester {
 
     void load();
     void detect();
+    void reject();
 
     void unknown();
 
@@ -159,6 +160,22 @@ const struct {
     {"XGL compressed", "thingy.zgl", "XglImporter"},
 };
 
+const struct {
+    const char* name;
+    const char* filename;
+} RejectData[]{
+    /* This lists pairs of filenames where, just based on extension, any
+       detection cannot be done */
+    {"COLLADA with a *.xml extension", "collada.xml"},
+    {"OGRE XML with just a *.xml extension", "mesh.xml"},
+    {"OGRE *.mesh", "ogre.mesh"},
+    {"Meshwork *.mesh", "foo.mesh"},
+    {"OBJ-like *.ter file", "terrain.ter"},
+    {"Terragen *.ter", "terragen.ter"},
+    {"Quake 1 *.mdl", "quake.mdl"},
+    {"3D Game Studio (3DGS) *.mdl", "3dgs.mdl"},
+};
+
 const struct {
     const char* name;
     ImporterFlags flags;
@@ -175,6 +192,9 @@ AnySceneImporterTest::AnySceneImporterTest() {
     addInstancedTests({&AnySceneImporterTest::detect},
         Containers::arraySize(DetectData));
 
+    addInstancedTests({&AnySceneImporterTest::reject},
+        Containers::arraySize(RejectData));
+
     addTests({&AnySceneImporterTest::unknown,
 
               &AnySceneImporterTest::propagateFlags,
@@ -270,6 +290,18 @@ void AnySceneImporterTest::detect() {
     #endif
 }
 
+void AnySceneImporterTest::reject() {
+    auto&& data = RejectData[testCaseInstanceId()];
+    setTestCaseDescription(data.name);
+
+    Containers::Pointer<AbstractImporter> importer = _manager.instantiate("AnySceneImporter");
+
+    Containers::String out;
+    Error redirectError{&out};
+    CORRADE_VERIFY(!importer->openFile(data.filename));
+    CORRADE_COMPARE(out, Utility::format("Trade::AnySceneImporter::openFile(): cannot determine the format of {}\n", data.filename));
+}
+
 void AnySceneImporterTest::unknown() {
     Containers::Pointer<AbstractImporter> importer = _manager.instantiate("AnySceneImporter");