diff --git a/doc/changelog.dox b/doc/changelog.dox
index 571a57247..93434578b 100644
--- a/doc/changelog.dox
+++ b/doc/changelog.dox
@@ -155,6 +155,8 @@ See also:
     [mosra/magnum#312](https://github.com/mosra/magnum/pull/312))
     @ref Trade::TgaImporter "TgaImporter" now properly reports an error message
     when opening an empty file
+-   @ref Trade::AbstractImporter::setFileCallback() now accepts callbacks with
+    @cpp const @ce references to user data as well
 
 @subsection changelog-latest-buildsystem Build system
 
diff --git a/src/Magnum/Trade/AbstractImporter.h b/src/Magnum/Trade/AbstractImporter.h
index f496306ba..5e6224edc 100644
--- a/src/Magnum/Trade/AbstractImporter.h
+++ b/src/Magnum/Trade/AbstractImporter.h
@@ -1239,7 +1239,7 @@ class MAGNUM_TRADE_EXPORT AbstractImporter: public PluginManager::AbstractManagi
         /* Used by the templated version only */
         struct FileCallbackTemplate {
             void(*callback)();
-            void* userData;
+            const void* userData;
         } _fileCallbackTemplate{};
 };
 
@@ -1250,10 +1250,10 @@ template<class Callback, class T> void AbstractImporter::setFileCallback(Callbac
     const auto callbackPtr = static_cast<Containers::Optional<Containers::ArrayView<const char>>(*)(const std::string&, InputFileCallbackPolicy, T&)>(callback);
     if(!callbackPtr) return setFileCallback(nullptr);
 
-    _fileCallbackTemplate = { reinterpret_cast<void(*)()>(callbackPtr), &userData };
+    _fileCallbackTemplate = { reinterpret_cast<void(*)()>(callbackPtr), static_cast<const void*>(&userData) };
     setFileCallback([](const std::string& filename, const InputFileCallbackPolicy flags, void* const userData) {
         auto& s = *reinterpret_cast<FileCallbackTemplate*>(userData);
-        return reinterpret_cast<Containers::Optional<Containers::ArrayView<const char>>(*)(const std::string&, InputFileCallbackPolicy, T&)>(s.callback)(filename, flags, *static_cast<T*>(s.userData));
+        return reinterpret_cast<Containers::Optional<Containers::ArrayView<const char>>(*)(const std::string&, InputFileCallbackPolicy, T&)>(s.callback)(filename, flags, *static_cast<T*>(const_cast<void*>(s.userData)));
     }, &_fileCallbackTemplate);
 }
 #endif
diff --git a/src/Magnum/Trade/Test/AbstractImporterTest.cpp b/src/Magnum/Trade/Test/AbstractImporterTest.cpp
index eb6909109..88ba5ca72 100644
--- a/src/Magnum/Trade/Test/AbstractImporterTest.cpp
+++ b/src/Magnum/Trade/Test/AbstractImporterTest.cpp
@@ -66,6 +66,7 @@ struct AbstractImporterTest: TestSuite::Tester {
     void setFileCallback();
     void setFileCallbackTemplate();
     void setFileCallbackTemplateNull();
+    void setFileCallbackTemplateConst();
     void setFileCallbackFileOpened();
     void setFileCallbackNotImplemented();
     void setFileCallbackNotSupported();
@@ -260,6 +261,7 @@ AbstractImporterTest::AbstractImporterTest() {
               &AbstractImporterTest::setFileCallback,
               &AbstractImporterTest::setFileCallbackTemplate,
               &AbstractImporterTest::setFileCallbackTemplateNull,
+              &AbstractImporterTest::setFileCallbackTemplateConst,
               &AbstractImporterTest::setFileCallbackFileOpened,
               &AbstractImporterTest::setFileCallbackNotImplemented,
               &AbstractImporterTest::setFileCallbackNotSupported,
@@ -665,6 +667,29 @@ void AbstractImporterTest::setFileCallbackTemplateNull() {
     CORRADE_VERIFY(importer.called);
 }
 
+void AbstractImporterTest::setFileCallbackTemplateConst() {
+    struct: AbstractImporter {
+        Features doFeatures() const override { return Feature::OpenData|Feature::FileCallback; }
+        bool doIsOpened() const override { return false; }
+        void doClose() override {}
+        void doSetFileCallback(Containers::Optional<Containers::ArrayView<const char>>(*)(const std::string&, InputFileCallbackPolicy, void*), void*) override {
+            called = true;
+        }
+
+        bool called = false;
+    } importer;
+
+    /* Just verify we can have const parameters */
+    const int a = 0;
+    auto lambda = [](const std::string&, InputFileCallbackPolicy, const int&) {
+        return Containers::Optional<Containers::ArrayView<const char>>{};
+    };
+    importer.setFileCallback(lambda, a);
+    CORRADE_VERIFY(importer.fileCallback());
+    CORRADE_VERIFY(importer.fileCallbackUserData());
+    CORRADE_VERIFY(importer.called);
+}
+
 void AbstractImporterTest::setFileCallbackFileOpened() {
     struct: AbstractImporter {
         Features doFeatures() const override { return {}; }