diff --git a/src/AbstractShaderProgram.h b/src/AbstractShaderProgram.h
index 814cf4d33..38b4f4866 100644
--- a/src/AbstractShaderProgram.h
+++ b/src/AbstractShaderProgram.h
@@ -1145,19 +1145,39 @@ template<std::size_t cols> struct SizedVectorAttribute {
 };
 template<> struct SizedAttribute<1, 1>: SizedVectorAttribute<1> {
     enum class Components: GLint { One = 1 };
-    constexpr static Components DefaultComponents = Components::One;
+    #ifndef CORRADE_GCC45_COMPATIBILITY
+    constexpr static
+    #else
+    static const
+    #endif
+    Components DefaultComponents = Components::One;
 };
 template<> struct SizedAttribute<1, 2>: SizedVectorAttribute<1> {
     enum class Components: GLint { One = 1, Two = 2 };
-    constexpr static Components DefaultComponents = Components::Two;
+    #ifndef CORRADE_GCC45_COMPATIBILITY
+    constexpr static
+    #else
+    static const
+    #endif
+    Components DefaultComponents = Components::Two;
 };
 template<> struct SizedAttribute<1, 3>: SizedVectorAttribute<1> {
     enum class Components: GLint { One = 1, Two = 2, Three = 3 };
-    constexpr static Components DefaultComponents = Components::Three;
+    #ifndef CORRADE_GCC45_COMPATIBILITY
+    constexpr static
+    #else
+    static const
+    #endif
+    Components DefaultComponents = Components::Three;
 };
 template<> struct SizedAttribute<1, 4>: SizedVectorAttribute<1> {
     enum class Components: GLint { One = 1, Two = 2, Three = 3, Four = 4 };
-    constexpr static Components DefaultComponents = Components::Four;
+    #ifndef CORRADE_GCC45_COMPATIBILITY
+    constexpr static
+    #else
+    static const
+    #endif
+    Components DefaultComponents = Components::Four;
 };
 Debug MAGNUM_EXPORT operator<<(Debug debug, SizedAttribute<1, 1>::Components value);
 Debug MAGNUM_EXPORT operator<<(Debug debug, SizedAttribute<1, 2>::Components value);
@@ -1168,15 +1188,30 @@ Debug MAGNUM_EXPORT operator<<(Debug debug, SizedAttribute<1, 4>::Components val
 template<std::size_t rows> struct SizedMatrixAttribute;
 template<> struct SizedMatrixAttribute<2> {
     enum class Components: GLint { Two   = 2 };
-    constexpr static Components DefaultComponents = Components::Two;
+    #ifndef CORRADE_GCC45_COMPATIBILITY
+    constexpr static
+    #else
+    static const
+    #endif
+    Components DefaultComponents = Components::Two;
 };
 template<> struct SizedMatrixAttribute<3> {
     enum class Components: GLint { Three = 3 };
-    constexpr static Components DefaultComponents = Components::Three;
+    #ifndef CORRADE_GCC45_COMPATIBILITY
+    constexpr static
+    #else
+    static const
+    #endif
+    Components DefaultComponents = Components::Three;
 };
 template<> struct SizedMatrixAttribute<4> {
     enum class Components: GLint { Four  = 4 };
-    constexpr static Components DefaultComponents = Components::Four;
+    #ifndef CORRADE_GCC45_COMPATIBILITY
+    constexpr static
+    #else
+    static const
+    #endif
+    Components DefaultComponents = Components::Four;
 };
 Debug MAGNUM_EXPORT operator<<(Debug debug, SizedMatrixAttribute<2>::Components value);
 Debug MAGNUM_EXPORT operator<<(Debug debug, SizedMatrixAttribute<3>::Components value);
@@ -1219,7 +1254,12 @@ struct FloatAttribute {
         Double = GL_DOUBLE
         #endif
     };
-    constexpr static DataType DefaultDataType = DataType::Float;
+    #ifndef CORRADE_GCC45_COMPATIBILITY
+    constexpr static
+    #else
+    static const
+    #endif
+    DataType DefaultDataType = DataType::Float;
 
     enum class DataOption: UnsignedByte {
         Normalized = 1 << 0
@@ -1246,7 +1286,12 @@ struct IntAttribute {
         UnsignedInt = GL_UNSIGNED_INT,
         Int = GL_INT
     };
-    constexpr static DataType DefaultDataType = DataType::Int;
+    #ifndef CORRADE_GCC45_COMPATIBILITY
+    constexpr static
+    #else
+    static const
+    #endif
+    DataType DefaultDataType = DataType::Int;
 
     enum class DataOption: UnsignedByte {};
     typedef Corrade::Containers::EnumSet<DataOption, UnsignedByte> DataOptions;
@@ -1261,7 +1306,12 @@ struct UnsignedIntAttribute {
     typedef UnsignedInt Type;
 
     typedef IntAttribute::DataType DataType;
-    constexpr static DataType DefaultDataType = DataType::UnsignedInt;
+    #ifndef CORRADE_GCC45_COMPATIBILITY
+    constexpr static
+    #else
+    static const
+    #endif
+    DataType DefaultDataType = DataType::UnsignedInt;
 
     typedef IntAttribute::DataOption DataOption;
     typedef Corrade::Containers::EnumSet<DataOption, UnsignedByte> DataOptions;
@@ -1280,7 +1330,12 @@ struct DoubleAttribute {
     enum class DataType: GLenum {
         Double = GL_DOUBLE
     };
-    constexpr static DataType DefaultDataType = DataType::Double;
+    #ifndef CORRADE_GCC45_COMPATIBILITY
+    constexpr static
+    #else
+    static const
+    #endif
+    DataType DefaultDataType = DataType::Double;
 
     enum class DataOption: UnsignedByte {};
     typedef Corrade::Containers::EnumSet<DataOption, UnsignedByte> DataOptions;
@@ -1305,7 +1360,12 @@ template<> struct Attribute<Math::Vector<4, Float>> {
         BGRA = GL_BGRA
         #endif
     };
-    constexpr static Components DefaultComponents = Components::Four;
+    #ifndef CORRADE_GCC45_COMPATIBILITY
+    constexpr static
+    #else
+    static const
+    #endif
+    Components DefaultComponents = Components::Four;
 
     enum class DataType: GLenum {
         UnsignedByte = GL_UNSIGNED_BYTE,
@@ -1330,7 +1390,12 @@ template<> struct Attribute<Math::Vector<4, Float>> {
         Int2101010Rev = GL_INT_2_10_10_10_REV
         #endif
     };
-    constexpr static DataType DefaultDataType = DataType::Float;
+    #ifndef CORRADE_GCC45_COMPATIBILITY
+    constexpr static
+    #else
+    static const
+    #endif
+    DataType DefaultDataType = DataType::Float;
 
     enum class DataOption: UnsignedByte {
         Normalized = 1 << 0
diff --git a/src/Math/Algorithms/Svd.h b/src/Math/Algorithms/Svd.h
index 9c4200515..5cde1de64 100644
--- a/src/Math/Algorithms/Svd.h
+++ b/src/Math/Algorithms/Svd.h
@@ -96,9 +96,14 @@ decomposition and least squares solutions"*.
 /* The matrix is passed by value because it is changed inside */
 template<std::size_t cols, std::size_t rows, class T> std::tuple<RectangularMatrix<cols, rows, T>, Vector<cols, T>, Matrix<cols, T>> svd(RectangularMatrix<cols, rows, T> m) {
     static_assert(rows >= cols, "Unsupported matrix aspect ratio");
-    static_assert(T(1)+TypeTraits<T>::epsilon() > T(1), "Epsilon too small");
     constexpr T tol = Implementation::smallestDelta<T>()/TypeTraits<T>::epsilon();
+    #ifndef CORRADE_GCC45_COMPATIBILITY
+    static_assert(T(1)+TypeTraits<T>::epsilon() > T(1), "Epsilon too small");
     static_assert(tol > T(0), "Tol too small");
+    #else
+    CORRADE_ASSERT(T(1)+TypeTraits<T>::epsilon() > T(1), "Epsilon too small", {});
+    CORRADE_ASSERT(tol > T(0), "Tol too small", {});
+    #endif
     constexpr std::size_t maxIterations = 50;
 
     Matrix<cols, T> v(Matrix<cols, T>::Zero);
diff --git a/src/MeshTools/Test/TransformTest.cpp b/src/MeshTools/Test/TransformTest.cpp
index 7d632c879..8c2569a7c 100644
--- a/src/MeshTools/Test/TransformTest.cpp
+++ b/src/MeshTools/Test/TransformTest.cpp
@@ -50,8 +50,8 @@ TransformTest::TransformTest() {
               &TransformTest::transformPoints3D});
 }
 
-/* GCC < 4.7 doesn't like constexpr here, don't know why */
-#ifdef CORRADE_GCC46_COMPATIBILITY
+/** @bug GCC < 4.7 doesn't like constexpr here, don't know why */
+#if defined(CORRADE_GCC46_COMPATIBILITY) && !defined(CORRADE_GCC45_COMPATIBILITY)
 #define constexpr const
 #endif
 
@@ -85,7 +85,7 @@ constexpr static std::array<Vector3, 2> points3DRotatedTranslated{{
     {15.0f,  1.5f,  1.5f}
 }};
 
-#ifdef CORRADE_GCC46_COMPATIBILITY
+#if defined(CORRADE_GCC46_COMPATIBILITY) && !defined(CORRADE_GCC45_COMPATIBILITY)
 #undef constexpr
 #endif
 
diff --git a/src/Test/SwizzleTest.cpp b/src/Test/SwizzleTest.cpp
index e340c3fa8..936740147 100644
--- a/src/Test/SwizzleTest.cpp
+++ b/src/Test/SwizzleTest.cpp
@@ -53,6 +53,11 @@ void SwizzleTest::type() {
     constexpr Color3<Float> origColor3;
     constexpr Color4<Double> origColor4;
 
+    /* decltype(a) is not const because a is not constexpr under GCC <= 4.5 */
+    #ifdef CORRADE_GCC45_COMPATIBILITY
+    #define const
+    #endif
+
     constexpr auto a = swizzle<'y', 'a'>(orig);
     CORRADE_VERIFY((std::is_same<decltype(a), const Vector2i>::value));
 
@@ -73,6 +78,10 @@ void SwizzleTest::type() {
 
     constexpr auto g = swizzle<'y', 'a', 'y', 'x'>(origColor4);
     CORRADE_VERIFY((std::is_same<decltype(g), const Color4<Double>>::value));
+
+    #ifdef CORRADE_GCC45_COMPATIBILITY
+    #undef const
+    #endif
 }
 
 void SwizzleTest::defaultType() {