diff --git a/src/Trade/AbstractImporter.h b/src/Trade/AbstractImporter.h
index 96612482d..6e78bd18e 100644
--- a/src/Trade/AbstractImporter.h
+++ b/src/Trade/AbstractImporter.h
@@ -100,15 +100,15 @@ class MAGNUM_EXPORT AbstractImporter: public Corrade::PluginManager::Plugin {
          * @brief Default scene
          *
          * When there is more than one scene, returns ID of the default one.
-         * Note that this function returns 0 even if there are no scenes.
+         * If there is no default scene, returns -1.
          *
          * @note The function is not const, because the value will probably
          *      be lazy-populated.
          */
-        virtual inline size_t defaultScene() { return 0; }
+        virtual inline int defaultScene() { return -1; }
 
         /** @brief %Scene count */
-        virtual inline size_t sceneCount() const { return 0; }
+        virtual inline unsigned int sceneCount() const { return 0; }
 
         /**
          * @brief %Scene
@@ -116,10 +116,10 @@ class MAGNUM_EXPORT AbstractImporter: public Corrade::PluginManager::Plugin {
          *
          * Returns pointer to given scene or nullptr, if no such scene exists.
          */
-        virtual inline SceneData* scene(size_t id) { return nullptr; }
+        virtual inline SceneData* scene(unsigned int id) { return nullptr; }
 
         /** @brief %Light count */
-        virtual inline size_t lightCount() const { return 0; }
+        virtual inline unsigned int lightCount() const { return 0; }
 
         /**
          * @brief %Light
@@ -127,10 +127,10 @@ class MAGNUM_EXPORT AbstractImporter: public Corrade::PluginManager::Plugin {
          *
          * Returns pointer to given light or nullptr, if no such light exists.
          */
-        virtual inline LightData* light(size_t id) { return nullptr; }
+        virtual inline LightData* light(unsigned int id) { return nullptr; }
 
         /** @brief %Camera count */
-        virtual inline size_t cameraCount() const { return 0; }
+        virtual inline unsigned int cameraCount() const { return 0; }
 
         /**
          * @brief %Camera
@@ -139,10 +139,10 @@ class MAGNUM_EXPORT AbstractImporter: public Corrade::PluginManager::Plugin {
          * Returns pointer to given camera or nullptr, if no such camera
          * exists.
          */
-        virtual inline CameraData* camera(size_t id) { return nullptr; }
+        virtual inline CameraData* camera(unsigned int id) { return nullptr; }
 
         /** @brief %Object count */
-        virtual inline size_t objectCount() const { return 0; }
+        virtual inline unsigned int objectCount() const { return 0; }
 
         /**
          * @brief %Object
@@ -151,10 +151,10 @@ class MAGNUM_EXPORT AbstractImporter: public Corrade::PluginManager::Plugin {
          * Returns pointer to given object or nullptr, if no such object
          * exists.
          */
-        virtual inline ObjectData* object(size_t id) { return nullptr; }
+        virtual inline ObjectData* object(unsigned int id) { return nullptr; }
 
         /** @brief %Mesh count */
-        virtual inline size_t meshCount() const { return 0; }
+        virtual inline unsigned int meshCount() const { return 0; }
 
         /**
          * @brief %Mesh
@@ -162,10 +162,10 @@ class MAGNUM_EXPORT AbstractImporter: public Corrade::PluginManager::Plugin {
          *
          * Returns pointer to given mesh or nullptr, if no such mesh exists.
          */
-        virtual inline MeshData* mesh(size_t id) { return nullptr; }
+        virtual inline MeshData* mesh(unsigned int id) { return nullptr; }
 
         /** @brief Material count */
-        virtual inline size_t materialCount() const { return 0; }
+        virtual inline unsigned int materialCount() const { return 0; }
 
         /**
          * @brief Material
@@ -174,10 +174,10 @@ class MAGNUM_EXPORT AbstractImporter: public Corrade::PluginManager::Plugin {
          * Returns pointer to given material or nullptr, if no such material
          * exists.
          */
-        virtual inline AbstractMaterialData* material(size_t id) { return nullptr; }
+        virtual inline AbstractMaterialData* material(unsigned int id) { return nullptr; }
 
         /** @brief %Texture count */
-        virtual inline size_t textureCount() const { return 0; }
+        virtual inline unsigned int textureCount() const { return 0; }
 
         /**
          * @brief %Texture
@@ -186,10 +186,10 @@ class MAGNUM_EXPORT AbstractImporter: public Corrade::PluginManager::Plugin {
          * Returns pointer to given texture or nullptr, if no such texture
          * exists.
          */
-        virtual inline TextureData* texture(size_t id) { return nullptr; }
+        virtual inline TextureData* texture(unsigned int id) { return nullptr; }
 
         /** @brief One-dimensional image count */
-        virtual inline size_t image1DCount() const { return 0; }
+        virtual inline unsigned int image1DCount() const { return 0; }
 
         /**
          * @brief One-dimensional image
@@ -197,10 +197,10 @@ class MAGNUM_EXPORT AbstractImporter: public Corrade::PluginManager::Plugin {
          *
          * Returns pointer to given image or nullptr, if no such image exists.
          */
-        virtual inline ImageData1D* image1D(size_t id) { return nullptr; }
+        virtual inline ImageData1D* image1D(unsigned int id) { return nullptr; }
 
         /** @brief Two-dimensional image count */
-        virtual inline size_t image2DCount() const { return 0; }
+        virtual inline unsigned int image2DCount() const { return 0; }
 
         /**
          * @brief Two-dimensional image
@@ -208,10 +208,10 @@ class MAGNUM_EXPORT AbstractImporter: public Corrade::PluginManager::Plugin {
          *
          * Returns pointer to given image or nullptr, if no such image exists.
          */
-        virtual inline ImageData2D* image2D(size_t id) { return nullptr; }
+        virtual inline ImageData2D* image2D(unsigned int id) { return nullptr; }
 
         /** @brief Three-dimensional image count */
-        virtual inline size_t image3DCount() const { return 0; }
+        virtual inline unsigned int image3DCount() const { return 0; }
 
         /**
          * @brief Three-dimensional image
@@ -219,7 +219,7 @@ class MAGNUM_EXPORT AbstractImporter: public Corrade::PluginManager::Plugin {
          *
          * Returns pointer to given image or nullptr, if no such image exists.
          */
-        virtual inline ImageData3D* image3D(size_t id) { return nullptr; }
+        virtual inline ImageData3D* image3D(unsigned int id) { return nullptr; }
 
         /*@}*/
 };
diff --git a/src/Trade/MeshData.h b/src/Trade/MeshData.h
index 6d7ad9ff3..f26f6b052 100644
--- a/src/Trade/MeshData.h
+++ b/src/Trade/MeshData.h
@@ -63,7 +63,7 @@ class MAGNUM_EXPORT MeshData {
         inline const std::vector<unsigned int>* indices() const { return _indices; } /**< @overload */
 
         /** @brief Count of vertex arrays */
-        inline size_t vertexArrayCount() const { return _vertices.size(); }
+        inline unsigned int vertexArrayCount() const { return _vertices.size(); }
 
         /**
          * @brief Vertices
@@ -71,11 +71,11 @@ class MAGNUM_EXPORT MeshData {
          * @return Vertices or nullptr if there is no vertex array with given
          *      ID.
          */
-        inline std::vector<Vector4>* vertices(size_t id) { return _vertices[id]; }
-        inline const std::vector<Vector4>* vertices(size_t id) const { return _vertices[id]; } /**< @overload */
+        inline std::vector<Vector4>* vertices(unsigned int id) { return _vertices[id]; }
+        inline const std::vector<Vector4>* vertices(unsigned int id) const { return _vertices[id]; } /**< @overload */
 
         /** @brief Count of normal arrays */
-        inline size_t normalArrayCount() const { return _normals.size(); }
+        inline unsigned int normalArrayCount() const { return _normals.size(); }
 
         /**
          * @brief Normals
@@ -83,11 +83,11 @@ class MAGNUM_EXPORT MeshData {
          * @return Vertices or nullptr if there is no normal array with given
          *      ID.
          */
-        inline std::vector<Vector3>* normals(size_t id) { return _normals[id]; }
-        inline const std::vector<Vector3>* normals(size_t id) const { return _normals[id]; } /**< @overload */
+        inline std::vector<Vector3>* normals(unsigned int id) { return _normals[id]; }
+        inline const std::vector<Vector3>* normals(unsigned int id) const { return _normals[id]; } /**< @overload */
 
         /** @brief Count of 2D texture coordinate arrays */
-        inline size_t textureCoords2DArrayCount() const { return _textureCoords2D.size(); }
+        inline unsigned int textureCoords2DArrayCount() const { return _textureCoords2D.size(); }
 
         /**
          * @brief 2D texture coordinates
@@ -95,8 +95,8 @@ class MAGNUM_EXPORT MeshData {
          * @return %Texture coordinates or nullptr if there is no texture
          *      coordinates array with given ID.
          */
-        inline std::vector<Vector2>* textureCoords2D(size_t id) { return _textureCoords2D[id]; }
-        inline const std::vector<Vector2>* textureCoords2D(size_t id) const { return _textureCoords2D[id]; } /**< @overload */
+        inline std::vector<Vector2>* textureCoords2D(unsigned int id) { return _textureCoords2D[id]; }
+        inline const std::vector<Vector2>* textureCoords2D(unsigned int id) const { return _textureCoords2D[id]; } /**< @overload */
 
     private:
         Mesh::Primitive _primitive;
diff --git a/src/Trade/MeshObjectData.h b/src/Trade/MeshObjectData.h
index d03482f93..91d59a631 100644
--- a/src/Trade/MeshObjectData.h
+++ b/src/Trade/MeshObjectData.h
@@ -44,13 +44,13 @@ class MeshObjectData: public ObjectData {
          *
          * Creates object with mesh instance type.
          */
-        inline MeshObjectData(std::vector<size_t> children, const Matrix4& transformation, size_t instance, size_t material): ObjectData(children, transformation, InstanceType::Mesh, instance), _material(material) {}
+        inline MeshObjectData(std::vector<unsigned int> children, const Matrix4& transformation, unsigned int instance, unsigned int material): ObjectData(children, transformation, InstanceType::Mesh, instance), _material(material) {}
 
         /** @brief Material ID */
-        inline size_t material() const { return _material; }
+        inline unsigned int material() const { return _material; }
 
     private:
-        size_t _material;
+        unsigned int _material;
 };
 
 }}
diff --git a/src/Trade/ObjectData.h b/src/Trade/ObjectData.h
index 3fce40481..69d40ff80 100644
--- a/src/Trade/ObjectData.h
+++ b/src/Trade/ObjectData.h
@@ -50,13 +50,13 @@ class ObjectData {
          * @param instanceType      Instance type
          * @param instanceId        Instance ID
          */
-        inline ObjectData(std::vector<size_t> children, const Matrix4& transformation, InstanceType instanceType, size_t instanceId): _children(children), _transformation(transformation), _instanceType(instanceType), _instanceId(instanceId) {}
+        inline ObjectData(std::vector<unsigned int> children, const Matrix4& transformation, InstanceType instanceType, unsigned int instanceId): _children(children), _transformation(transformation), _instanceType(instanceType), _instanceId(instanceId) {}
 
         /** @brief Destructor */
         inline virtual ~ObjectData() {}
 
         /** @brief Child objects */
-        inline std::vector<size_t>& children() { return _children; }
+        inline std::vector<unsigned int>& children() { return _children; }
 
         /** @brief Transformation (relative to parent) */
         inline Matrix4 transformation() const { return _transformation; }
@@ -75,13 +75,13 @@ class ObjectData {
          * @return ID of given camera / light / mesh etc., specified by
          *      instanceType()
          */
-        inline size_t instanceId() const { return _instanceId; }
+        inline unsigned int instanceId() const { return _instanceId; }
 
     private:
-        std::vector<size_t> _children;
+        std::vector<unsigned int> _children;
         Matrix4 _transformation;
         InstanceType _instanceType;
-        size_t _instanceId;
+        unsigned int _instanceId;
 };
 
 }}
diff --git a/src/Trade/SceneData.h b/src/Trade/SceneData.h
index 1916fe607..c2cd786fd 100644
--- a/src/Trade/SceneData.h
+++ b/src/Trade/SceneData.h
@@ -37,13 +37,13 @@ class MAGNUM_EXPORT SceneData {
          * @brief Constructor
          * @param children  Child objects
          */
-        inline SceneData(const std::vector<size_t>& children): _children(children) {}
+        inline SceneData(const std::vector<unsigned int>& children): _children(children) {}
 
         /** @brief Child objects */
-        inline const std::vector<size_t>& children() const { return _children; }
+        inline const std::vector<unsigned int>& children() const { return _children; }
 
     private:
-        std::vector<size_t> _children;
+        std::vector<unsigned int> _children;
 };
 
 }}