diff --git a/src/AbstractTexture.cpp b/src/AbstractTexture.cpp
index c97bbc0f0..3d7c33135 100644
--- a/src/AbstractTexture.cpp
+++ b/src/AbstractTexture.cpp
@@ -124,8 +124,12 @@ Int AbstractTexture::maxIntegerSamples() {
 }
 #endif
 
-void AbstractTexture::destroy() {
-    /* Moved out */
+AbstractTexture::AbstractTexture(GLenum target): _target(target) {
+    glGenTextures(1, &_id);
+}
+
+AbstractTexture::~AbstractTexture() {
+    /* Moved out, nothing to do */
     if(!_id) return;
 
     /* Remove all bindings */
@@ -135,30 +139,6 @@ void AbstractTexture::destroy() {
     glDeleteTextures(1, &_id);
 }
 
-void AbstractTexture::move() {
-    _id = 0;
-}
-
-AbstractTexture::AbstractTexture(GLenum target): _target(target) {
-    glGenTextures(1, &_id);
-}
-
-AbstractTexture::~AbstractTexture() { destroy(); }
-
-AbstractTexture::AbstractTexture(AbstractTexture&& other): _target(other._target), _id(other._id) {
-    other.move();
-}
-
-AbstractTexture& AbstractTexture::operator=(AbstractTexture&& other) {
-    destroy();
-
-    _target = other._target;
-    _id = other._id;
-
-    other.move();
-    return *this;
-}
-
 std::string AbstractTexture::label() const {
     return Context::current()->state().debug->getLabelImplementation(GL_TEXTURE, _id);
 }
diff --git a/src/AbstractTexture.h b/src/AbstractTexture.h
index 495aeef00..95b4cd4b0 100644
--- a/src/AbstractTexture.h
+++ b/src/AbstractTexture.h
@@ -158,13 +158,13 @@ class MAGNUM_EXPORT AbstractTexture: public AbstractObject {
         AbstractTexture(const AbstractTexture&) = delete;
 
         /** @brief Move constructor */
-        AbstractTexture(AbstractTexture&& other);
+        AbstractTexture(AbstractTexture&& other) noexcept;
 
         /** @brief Copying is not allowed */
         AbstractTexture& operator=(const AbstractTexture&) = delete;
 
         /** @brief Move assignment */
-        AbstractTexture& operator=(AbstractTexture&& other);
+        AbstractTexture& operator=(AbstractTexture&& other) noexcept;
 
         /**
          * @brief %Texture label
@@ -482,8 +482,6 @@ class MAGNUM_EXPORT AbstractTexture: public AbstractObject {
         #endif
         static InvalidateSubImageImplementation invalidateSubImageImplementation;
 
-        void MAGNUM_LOCAL destroy();
-        void MAGNUM_LOCAL move();
         ColorFormat MAGNUM_LOCAL imageFormatForInternalFormat(TextureFormat internalFormat);
         ColorType MAGNUM_LOCAL imageTypeForInternalFormat(TextureFormat internalFormat);
 
@@ -597,6 +595,16 @@ template<> struct MAGNUM_EXPORT AbstractTexture::DataHelper<3> {
 };
 #endif
 
+inline AbstractTexture::AbstractTexture(AbstractTexture&& other) noexcept: _target(other._target), _id(other._id) {
+    other._id = 0;
+}
+
+inline AbstractTexture& AbstractTexture::operator=(AbstractTexture&& other) noexcept {
+    std::swap(_target, other._target);
+    std::swap(_id, other._id);
+    return *this;
+}
+
 }
 
 #endif
diff --git a/src/BufferTexture.h b/src/BufferTexture.h
index ac9d37286..f53c01e29 100644
--- a/src/BufferTexture.h
+++ b/src/BufferTexture.h
@@ -201,11 +201,6 @@ and respective function documentation for more information.
 class MAGNUM_EXPORT BufferTexture: private AbstractTexture {
     friend class Context;
 
-    BufferTexture(const BufferTexture&) = delete;
-    BufferTexture(BufferTexture&&) = delete;
-    BufferTexture& operator=(const BufferTexture&) = delete;
-    BufferTexture& operator=(BufferTexture&&) = delete;
-
     public:
         /** @copydoc AbstractTexture::maxLabelLength() */
         static Int maxLabelLength() { return AbstractTexture::maxLabelLength(); }
diff --git a/src/Test/AbstractTextureGLTest.cpp b/src/Test/AbstractTextureGLTest.cpp
index fdf8d9539..42865ae14 100644
--- a/src/Test/AbstractTextureGLTest.cpp
+++ b/src/Test/AbstractTextureGLTest.cpp
@@ -33,11 +33,57 @@ class AbstractTextureGLTest: public AbstractOpenGLTester {
     public:
         explicit AbstractTextureGLTest();
 
+        void construct();
+        void constructCopy();
+        void constructMove();
+
         void label();
 };
 
 AbstractTextureGLTest::AbstractTextureGLTest() {
-    addTests({&AbstractTextureGLTest::label});
+    addTests({&AbstractTextureGLTest::construct,
+              &AbstractTextureGLTest::constructCopy,
+              &AbstractTextureGLTest::constructMove,
+
+              &AbstractTextureGLTest::label});
+}
+
+void AbstractTextureGLTest::construct() {
+    {
+        const Texture2D texture;
+
+        MAGNUM_VERIFY_NO_ERROR();
+        CORRADE_VERIFY(texture.id() > 0);
+    }
+
+    MAGNUM_VERIFY_NO_ERROR();
+}
+
+void AbstractTextureGLTest::constructCopy() {
+     CORRADE_VERIFY(!(std::is_constructible<Texture2D, const Texture2D&>{}));
+     CORRADE_VERIFY(!(std::is_assignable<Texture2D, const Texture2D&>{}));
+}
+
+void AbstractTextureGLTest::constructMove() {
+    Texture2D a;
+    const Int id = a.id();
+
+    MAGNUM_VERIFY_NO_ERROR();
+    CORRADE_VERIFY(id > 0);
+
+    Texture2D b(std::move(a));
+
+    CORRADE_COMPARE(a.id(), 0);
+    CORRADE_COMPARE(b.id(), id);
+
+    Texture2D c;
+    const Int cId = c.id();
+    c = std::move(b);
+
+    MAGNUM_VERIFY_NO_ERROR();
+    CORRADE_VERIFY(cId > 0);
+    CORRADE_COMPARE(b.id(), cId);
+    CORRADE_COMPARE(c.id(), id);
 }
 
 void AbstractTextureGLTest::label() {