diff --git a/include/SFML/Graphics/Shape.hpp b/include/SFML/Graphics/Shape.hpp
index 51686aa7f..23e3375b1 100644
--- a/include/SFML/Graphics/Shape.hpp
+++ b/include/SFML/Graphics/Shape.hpp
@@ -46,12 +46,6 @@ class Texture;
 class SFML_GRAPHICS_API Shape : public Drawable, public Transformable
 {
 public:
-    ////////////////////////////////////////////////////////////
-    /// \brief Virtual destructor
-    ///
-    ////////////////////////////////////////////////////////////
-    ~Shape() override;
-
     ////////////////////////////////////////////////////////////
     /// \brief Change the source texture of the shape
     ///
diff --git a/include/SFML/Graphics/Texture.hpp b/include/SFML/Graphics/Texture.hpp
index ea387875c..1ecc1e716 100644
--- a/include/SFML/Graphics/Texture.hpp
+++ b/include/SFML/Graphics/Texture.hpp
@@ -518,7 +518,7 @@ public:
     /// \param right Instance to swap with
     ///
     ////////////////////////////////////////////////////////////
-    void swap(Texture& right);
+    void swap(Texture& right) noexcept;
 
     ////////////////////////////////////////////////////////////
     /// \brief Get the underlying OpenGL handle of the texture.
@@ -621,6 +621,15 @@ private:
     std::uint64_t m_cacheId;         //!< Unique number that identifies the texture to the render target's cache
 };
 
+////////////////////////////////////////////////////////////
+/// \brief Swap the contents of one texture with those of another
+///
+/// \param left First instance to swap
+/// \param right Second instance to swap
+///
+////////////////////////////////////////////////////////////
+void swap(Texture& left, Texture& right) noexcept;
+
 } // namespace sf
 
 
diff --git a/include/SFML/Graphics/VertexBuffer.hpp b/include/SFML/Graphics/VertexBuffer.hpp
index 0e8459814..a76a4098c 100644
--- a/include/SFML/Graphics/VertexBuffer.hpp
+++ b/include/SFML/Graphics/VertexBuffer.hpp
@@ -224,7 +224,7 @@ public:
     /// \param right Instance to swap with
     ///
     ////////////////////////////////////////////////////////////
-    void swap(VertexBuffer& right);
+    void swap(VertexBuffer& right) noexcept;
 
     ////////////////////////////////////////////////////////////
     /// \brief Get the underlying OpenGL handle of the vertex buffer.
@@ -338,6 +338,15 @@ private:
     Usage         m_usage{Stream};                        //!< How this vertex buffer is to be used
 };
 
+////////////////////////////////////////////////////////////
+/// \brief Swap the contents of one vertex buffer with those of another
+///
+/// \param left First instance to swap
+/// \param right Second instance to swap
+///
+////////////////////////////////////////////////////////////
+void swap(VertexBuffer& left, VertexBuffer& right) noexcept;
+
 } // namespace sf
 
 
diff --git a/src/SFML/Graphics/CMakeLists.txt b/src/SFML/Graphics/CMakeLists.txt
index e595331aa..a72408b32 100644
--- a/src/SFML/Graphics/CMakeLists.txt
+++ b/src/SFML/Graphics/CMakeLists.txt
@@ -126,6 +126,17 @@ endif()
 sfml_find_package(Freetype INCLUDE "FREETYPE_INCLUDE_DIRS" LINK "FREETYPE_LIBRARY")
 target_link_libraries(sfml-graphics PRIVATE Freetype)
 
+# on some platforms (e.g. Raspberry Pi 3 armhf), GCC requires linking libatomic to use <atomic> features
+# that aren't supported by native CPU instructions (64-bit atomic operations on 32-bit architecture)
+if(SFML_COMPILER_GCC)
+    include(CheckCXXSourceCompiles)
+    check_cxx_source_compiles("#include <atomic>
+        int main(){std::atomic_ullong x(1); return x.fetch_add(1);}" ATOMIC_TEST)
+    if(NOT ATOMIC_TEST)
+        target_link_libraries(sfml-graphics PRIVATE atomic)
+    endif()
+endif()
+
 # add preprocessor symbols
 target_compile_definitions(sfml-graphics PRIVATE "STBI_FAILURE_USERMSG")
 
diff --git a/src/SFML/Graphics/Shape.cpp b/src/SFML/Graphics/Shape.cpp
index 94c99cd1f..749071bcd 100644
--- a/src/SFML/Graphics/Shape.cpp
+++ b/src/SFML/Graphics/Shape.cpp
@@ -48,10 +48,6 @@ sf::Vector2f computeNormal(const sf::Vector2f& p1, const sf::Vector2f& p2)
 
 namespace sf
 {
-////////////////////////////////////////////////////////////
-Shape::~Shape() = default;
-
-
 ////////////////////////////////////////////////////////////
 void Shape::setTexture(const Texture* texture, bool resetRect)
 {
diff --git a/src/SFML/Graphics/Texture.cpp b/src/SFML/Graphics/Texture.cpp
index 5cc113eff..ed1346015 100644
--- a/src/SFML/Graphics/Texture.cpp
+++ b/src/SFML/Graphics/Texture.cpp
@@ -33,10 +33,10 @@
 #include <SFML/Window/Context.hpp>
 #include <SFML/Window/Window.hpp>
 
+#include <atomic>
 #include <cassert>
 #include <climits>
 #include <cstring>
-#include <mutex>
 #include <ostream>
 
 
@@ -45,18 +45,13 @@ namespace
 // A nested named namespace is used here to allow unity builds of SFML.
 namespace TextureImpl
 {
-std::recursive_mutex idMutex;
-std::recursive_mutex maximumSizeMutex;
-
 // Thread-safe unique identifier generator,
 // is used for states cache (see RenderTarget)
-std::uint64_t getUniqueId()
+std::uint64_t getUniqueId() noexcept
 {
-    std::lock_guard lock(idMutex);
+    static std::atomic<std::uint64_t> id(1); // start at 1, zero is "no texture"
 
-    static std::uint64_t id = 1; // start at 1, zero is "no texture"
-
-    return id++;
+    return id.fetch_add(1);
 }
 } // namespace TextureImpl
 } // namespace
@@ -832,21 +827,18 @@ void Texture::bind(const Texture* texture, CoordinateType coordinateType)
 ////////////////////////////////////////////////////////////
 unsigned int Texture::getMaximumSize()
 {
-    std::lock_guard lock(TextureImpl::maximumSizeMutex);
-
-    static bool  checked = false;
-    static GLint size    = 0;
-
-    if (!checked)
+    static const unsigned int size = []()
     {
-        checked = true;
-
         TransientContextLock transientLock;
 
-        glCheck(glGetIntegerv(GL_MAX_TEXTURE_SIZE, &size));
-    }
+        GLint value = 0;
 
-    return static_cast<unsigned int>(size);
+        glCheck(glGetIntegerv(GL_MAX_TEXTURE_SIZE, &value));
+
+        return static_cast<unsigned int>(value);
+    }();
+
+    return size;
 }
 
 
@@ -862,7 +854,7 @@ Texture& Texture::operator=(const Texture& right)
 
 
 ////////////////////////////////////////////////////////////
-void Texture::swap(Texture& right)
+void Texture::swap(Texture& right) noexcept
 {
     std::swap(m_size, right.m_size);
     std::swap(m_actualSize, right.m_actualSize);
@@ -905,4 +897,11 @@ unsigned int Texture::getValidSize(unsigned int size)
     }
 }
 
+
+////////////////////////////////////////////////////////////
+void swap(Texture& left, Texture& right) noexcept
+{
+    left.swap(right);
+}
+
 } // namespace sf
diff --git a/src/SFML/Graphics/VertexBuffer.cpp b/src/SFML/Graphics/VertexBuffer.cpp
index ccc4fbe81..8d3cd5c65 100644
--- a/src/SFML/Graphics/VertexBuffer.cpp
+++ b/src/SFML/Graphics/VertexBuffer.cpp
@@ -33,7 +33,6 @@
 
 #include <cstddef>
 #include <cstring>
-#include <mutex>
 #include <ostream>
 #include <utility>
 
@@ -42,8 +41,6 @@ namespace
 // A nested named namespace is used here to allow unity builds of SFML.
 namespace VertexBufferImpl
 {
-std::recursive_mutex isAvailableMutex;
-
 GLenum usageToGlEnum(sf::VertexBuffer::Usage usage)
 {
     switch (usage)
@@ -274,7 +271,7 @@ VertexBuffer& VertexBuffer::operator=(const VertexBuffer& right)
 
 
 ////////////////////////////////////////////////////////////
-void VertexBuffer::swap(VertexBuffer& right)
+void VertexBuffer::swap(VertexBuffer& right) noexcept
 {
     std::swap(m_size, right.m_size);
     std::swap(m_buffer, right.m_buffer);
@@ -333,22 +330,15 @@ VertexBuffer::Usage VertexBuffer::getUsage() const
 ////////////////////////////////////////////////////////////
 bool VertexBuffer::isAvailable()
 {
-    std::lock_guard lock(VertexBufferImpl::isAvailableMutex);
-
-    static bool checked   = false;
-    static bool available = false;
-
-    if (!checked)
+    static const bool available = []() -> bool
     {
-        checked = true;
-
         TransientContextLock contextLock;
 
         // Make sure that extensions are initialized
         sf::priv::ensureExtensionsInit();
 
-        available = GLEXT_vertex_buffer_object;
-    }
+        return GLEXT_vertex_buffer_object;
+    }();
 
     return available;
 }
@@ -361,4 +351,11 @@ void VertexBuffer::draw(RenderTarget& target, const RenderStates& states) const
         target.draw(*this, 0, m_size, states);
 }
 
+
+////////////////////////////////////////////////////////////
+void swap(VertexBuffer& left, VertexBuffer& right) noexcept
+{
+    left.swap(right);
+}
+
 } // namespace sf
diff --git a/test/Graphics/CircleShape.test.cpp b/test/Graphics/CircleShape.test.cpp
index 3f766126f..20b225afa 100644
--- a/test/Graphics/CircleShape.test.cpp
+++ b/test/Graphics/CircleShape.test.cpp
@@ -7,8 +7,8 @@
 
 static_assert(std::is_copy_constructible_v<sf::CircleShape>);
 static_assert(std::is_copy_assignable_v<sf::CircleShape>);
-static_assert(std::is_move_constructible_v<sf::CircleShape>);
-static_assert(std::is_move_assignable_v<sf::CircleShape>);
+static_assert(std::is_nothrow_move_constructible_v<sf::CircleShape>);
+static_assert(std::is_nothrow_move_assignable_v<sf::CircleShape>);
 
 TEST_CASE("[Graphics] sf::CircleShape")
 {
diff --git a/test/Graphics/ConvexShape.test.cpp b/test/Graphics/ConvexShape.test.cpp
index 04e7cbb9c..29329c96d 100644
--- a/test/Graphics/ConvexShape.test.cpp
+++ b/test/Graphics/ConvexShape.test.cpp
@@ -7,8 +7,8 @@
 
 static_assert(std::is_copy_constructible_v<sf::ConvexShape>);
 static_assert(std::is_copy_assignable_v<sf::ConvexShape>);
-static_assert(std::is_move_constructible_v<sf::ConvexShape>);
-static_assert(std::is_move_assignable_v<sf::ConvexShape>);
+static_assert(std::is_nothrow_move_constructible_v<sf::ConvexShape>);
+static_assert(std::is_nothrow_move_assignable_v<sf::ConvexShape>);
 
 TEST_CASE("[Graphics] sf::ConvexShape")
 {
diff --git a/test/Graphics/RectangleShape.test.cpp b/test/Graphics/RectangleShape.test.cpp
index 0a49d23a4..9fe3ebe1c 100644
--- a/test/Graphics/RectangleShape.test.cpp
+++ b/test/Graphics/RectangleShape.test.cpp
@@ -7,8 +7,8 @@
 
 static_assert(std::is_copy_constructible_v<sf::RectangleShape>);
 static_assert(std::is_copy_assignable_v<sf::RectangleShape>);
-static_assert(std::is_move_constructible_v<sf::RectangleShape>);
-static_assert(std::is_move_assignable_v<sf::RectangleShape>);
+static_assert(std::is_nothrow_move_constructible_v<sf::RectangleShape>);
+static_assert(std::is_nothrow_move_assignable_v<sf::RectangleShape>);
 
 TEST_CASE("[Graphics] sf::RectangleShape")
 {
diff --git a/test/Graphics/Shape.test.cpp b/test/Graphics/Shape.test.cpp
index 411426280..495f8445d 100644
--- a/test/Graphics/Shape.test.cpp
+++ b/test/Graphics/Shape.test.cpp
@@ -9,7 +9,8 @@ static_assert(!std::is_constructible_v<sf::Shape>);
 static_assert(!std::is_copy_constructible_v<sf::Shape>);
 static_assert(std::is_copy_assignable_v<sf::Shape>);
 static_assert(!std::is_move_constructible_v<sf::Shape>);
-static_assert(std::is_move_assignable_v<sf::Shape>);
+static_assert(std::is_nothrow_move_assignable_v<sf::Shape>);
+static_assert(std::has_virtual_destructor_v<sf::Shape>);
 
 class TriangleShape : public sf::Shape
 {
diff --git a/test/Graphics/Texture.test.cpp b/test/Graphics/Texture.test.cpp
index 20ac4aef2..729aebe66 100644
--- a/test/Graphics/Texture.test.cpp
+++ b/test/Graphics/Texture.test.cpp
@@ -11,6 +11,7 @@ static_assert(std::is_move_constructible_v<sf::Texture>);
 static_assert(!std::is_nothrow_move_constructible_v<sf::Texture>);
 static_assert(std::is_move_assignable_v<sf::Texture>);
 static_assert(!std::is_nothrow_move_assignable_v<sf::Texture>);
+static_assert(std::is_nothrow_swappable_v<sf::Texture>);
 
 TEST_CASE("[Graphics] sf::Texture" * doctest::skip(skipDisplayTests))
 {
diff --git a/test/Graphics/VertexBuffer.test.cpp b/test/Graphics/VertexBuffer.test.cpp
index 63f20dbf0..2d3521427 100644
--- a/test/Graphics/VertexBuffer.test.cpp
+++ b/test/Graphics/VertexBuffer.test.cpp
@@ -15,6 +15,7 @@ static_assert(std::is_move_constructible_v<sf::VertexBuffer>);
 static_assert(!std::is_nothrow_move_constructible_v<sf::VertexBuffer>);
 static_assert(std::is_move_assignable_v<sf::VertexBuffer>);
 static_assert(!std::is_nothrow_move_assignable_v<sf::VertexBuffer>);
+static_assert(std::is_nothrow_swappable_v<sf::VertexBuffer>);
 
 // Skip these tests because they produce flakey failures in CI when using xvfb-run
 TEST_CASE("[Graphics] sf::VertexBuffer" * doctest::skip(true))
@@ -148,7 +149,7 @@ TEST_CASE("[Graphics] sf::VertexBuffer" * doctest::skip(true))
         sf::VertexBuffer vertexBuffer2(sf::PrimitiveType::TriangleStrip, sf::VertexBuffer::Stream);
         CHECK(vertexBuffer2.create(60));
 
-        vertexBuffer1.swap(vertexBuffer2);
+        std::swap(vertexBuffer1, vertexBuffer2);
 
         CHECK(vertexBuffer1.getVertexCount() == 60);
         CHECK(vertexBuffer1.getNativeHandle() != 0);