diff --git a/modules/juce_graphics/contexts/juce_GraphicsContext.cpp b/modules/juce_graphics/contexts/juce_GraphicsContext.cpp
index 2efb3aa991..fd45ad824e 100644
--- a/modules/juce_graphics/contexts/juce_GraphicsContext.cpp
+++ b/modules/juce_graphics/contexts/juce_GraphicsContext.cpp
@@ -25,7 +25,7 @@
 namespace
 {
     template <typename Type>
-    Rectangle<Type> coordsToRectangle (Type x, Type y, Type w, Type h)
+    Rectangle<Type> coordsToRectangle (Type x, Type y, Type w, Type h) noexcept
     {
        #if JUCE_DEBUG
         const int maxVal = 0x3fffffff;
@@ -77,7 +77,7 @@ bool Graphics::isVectorDevice() const
     return context.isVectorDevice();
 }
 
-bool Graphics::reduceClipRegion (const Rectangle<int>& area)
+bool Graphics::reduceClipRegion (Rectangle<int> area)
 {
     saveStateIfPending();
     return context.clipToRectangle (area);
@@ -85,7 +85,7 @@ bool Graphics::reduceClipRegion (const Rectangle<int>& area)
 
 bool Graphics::reduceClipRegion (const int x, const int y, const int w, const int h)
 {
-    return reduceClipRegion (Rectangle<int> (x, y, w, h));
+    return reduceClipRegion (coordsToRectangle (x, y, w, h));
 }
 
 bool Graphics::reduceClipRegion (const RectangleList<int>& clipRegion)
@@ -108,7 +108,7 @@ bool Graphics::reduceClipRegion (const Image& image, const AffineTransform& tran
     return ! context.isClipEmpty();
 }
 
-void Graphics::excludeClipRegion (const Rectangle<int>& rectangleToExclude)
+void Graphics::excludeClipRegion (Rectangle<int> rectangleToExclude)
 {
     saveStateIfPending();
     context.excludeClipRectangle (rectangleToExclude);
@@ -164,7 +164,7 @@ void Graphics::addTransform (const AffineTransform& transform)
     context.addTransform (transform);
 }
 
-bool Graphics::clipRegionIntersects (const Rectangle<int>& area) const
+bool Graphics::clipRegionIntersects (Rectangle<int> area) const
 {
     return context.clipRegionIntersects (area);
 }
@@ -281,7 +281,7 @@ void Graphics::drawMultiLineText (const String& text, const int startX,
     }
 }
 
-void Graphics::drawText (const String& text, const Rectangle<float>& area,
+void Graphics::drawText (const String& text, Rectangle<float> area,
                          Justification justificationType, bool useEllipsesIfTooBig) const
 {
     if (text.isNotEmpty() && context.clipRegionIntersects (area.getSmallestIntegerContainer()))
@@ -297,19 +297,19 @@ void Graphics::drawText (const String& text, const Rectangle<float>& area,
     }
 }
 
-void Graphics::drawText (const String& text, const Rectangle<int>& area,
+void Graphics::drawText (const String& text, Rectangle<int> area,
                          Justification justificationType, bool useEllipsesIfTooBig) const
 {
     drawText (text, area.toFloat(), justificationType, useEllipsesIfTooBig);
 }
 
-void Graphics::drawText (const String& text, const int x, const int y, const int width, const int height,
+void Graphics::drawText (const String& text, int x, int y, int width, int height,
                          Justification justificationType, const bool useEllipsesIfTooBig) const
 {
-    drawText (text, Rectangle<int> (x, y, width, height), justificationType, useEllipsesIfTooBig);
+    drawText (text, coordsToRectangle (x, y, width, height), justificationType, useEllipsesIfTooBig);
 }
 
-void Graphics::drawFittedText (const String& text, const Rectangle<int>& area,
+void Graphics::drawFittedText (const String& text, Rectangle<int> area,
                                Justification justification,
                                const int maximumNumberOfLines,
                                const float minimumHorizontalScale) const
@@ -328,7 +328,7 @@ void Graphics::drawFittedText (const String& text, const Rectangle<int>& area,
     }
 }
 
-void Graphics::drawFittedText (const String& text, const int x, const int y, const int width, const int height,
+void Graphics::drawFittedText (const String& text, int x, int y, int width, int height,
                                Justification justification,
                                const int maximumNumberOfLines,
                                const float minimumHorizontalScale) const
@@ -338,12 +338,12 @@ void Graphics::drawFittedText (const String& text, const int x, const int y, con
 }
 
 //==============================================================================
-void Graphics::fillRect (const Rectangle<int>& r) const
+void Graphics::fillRect (Rectangle<int> r) const
 {
     context.fillRect (r, false);
 }
 
-void Graphics::fillRect (const Rectangle<float>& r) const
+void Graphics::fillRect (Rectangle<float> r) const
 {
     context.fillRect (r);
 }
@@ -371,7 +371,7 @@ void Graphics::fillRectList (const RectangleList<int>& rects) const
 
 void Graphics::setPixel (int x, int y) const
 {
-    context.fillRect (Rectangle<int> (x, y, 1, 1), false);
+    context.fillRect (coordsToRectangle (x, y, 1, 1), false);
 }
 
 void Graphics::fillAll() const
@@ -426,7 +426,7 @@ void Graphics::drawRect (int x, int y, int width, int height, int lineThickness)
     drawRect (coordsToRectangle (x, y, width, height), lineThickness);
 }
 
-void Graphics::drawRect (const Rectangle<int>& r, int lineThickness) const
+void Graphics::drawRect (Rectangle<int> r, int lineThickness) const
 {
     drawRect (r.toFloat(), (float) lineThickness);
 }
@@ -444,7 +444,7 @@ void Graphics::drawRect (Rectangle<float> r, const float lineThickness) const
 }
 
 //==============================================================================
-void Graphics::fillEllipse (const Rectangle<float>& area) const
+void Graphics::fillEllipse (Rectangle<float> area) const
 {
     Path p;
     p.addEllipse (area);
@@ -453,19 +453,31 @@ void Graphics::fillEllipse (const Rectangle<float>& area) const
 
 void Graphics::fillEllipse (float x, float y, float w, float h) const
 {
-    fillEllipse (Rectangle<float> (x, y, w, h));
+    fillEllipse (coordsToRectangle (x, y, w, h));
 }
 
 void Graphics::drawEllipse (float x, float y, float width, float height, float lineThickness) const
 {
-    Path p;
-    p.addEllipse (x, y, width, height);
-    strokePath (p, PathStrokeType (lineThickness));
+    drawEllipse (coordsToRectangle (x, y, width, height), lineThickness);
 }
 
-void Graphics::drawEllipse (const Rectangle<float>& area, float lineThickness) const
+void Graphics::drawEllipse (Rectangle<float> area, float lineThickness) const
 {
-    drawEllipse (area.getX(), area.getY(), area.getWidth(), area.getHeight(), lineThickness);
+    Path p;
+
+    if (area.getWidth() == area.getHeight())
+    {
+        // For a circle, we can avoid having to generate a stroke
+        p.addEllipse (area.expanded (lineThickness * 0.5f));
+        p.addEllipse (area.reduced  (lineThickness * 0.5f));
+        p.setUsingNonZeroWinding (false);
+        fillPath (p);
+    }
+    else
+    {
+        p.addEllipse (area);
+        strokePath (p, PathStrokeType (lineThickness));
+    }
 }
 
 void Graphics::fillRoundedRectangle (float x, float y, float width, float height, float cornerSize) const
@@ -473,7 +485,7 @@ void Graphics::fillRoundedRectangle (float x, float y, float width, float height
     fillRoundedRectangle (coordsToRectangle (x, y, width, height), cornerSize);
 }
 
-void Graphics::fillRoundedRectangle (const Rectangle<float>& r, const float cornerSize) const
+void Graphics::fillRoundedRectangle (Rectangle<float> r, const float cornerSize) const
 {
     Path p;
     p.addRoundedRectangle (r, cornerSize);
@@ -486,7 +498,7 @@ void Graphics::drawRoundedRectangle (float x, float y, float width, float height
     drawRoundedRectangle (coordsToRectangle (x, y, width, height), cornerSize, lineThickness);
 }
 
-void Graphics::drawRoundedRectangle (const Rectangle<float>& r, float cornerSize, float lineThickness) const
+void Graphics::drawRoundedRectangle (Rectangle<float> r, float cornerSize, float lineThickness) const
 {
     Path p;
     p.addRoundedRectangle (r, cornerSize);
@@ -500,7 +512,7 @@ void Graphics::drawArrow (const Line<float>& line, float lineThickness, float ar
     fillPath (p);
 }
 
-void Graphics::fillCheckerBoard (const Rectangle<int>& area,
+void Graphics::fillCheckerBoard (Rectangle<int> area,
                                  const int checkWidth, const int checkHeight,
                                  Colour colour1, Colour colour2) const
 {
diff --git a/modules/juce_graphics/contexts/juce_GraphicsContext.h b/modules/juce_graphics/contexts/juce_GraphicsContext.h
index 3cfcc8cf62..9c89b9370f 100644
--- a/modules/juce_graphics/contexts/juce_GraphicsContext.h
+++ b/modules/juce_graphics/contexts/juce_GraphicsContext.h
@@ -170,7 +170,7 @@ public:
         @see drawSingleLineText, drawFittedText, drawMultiLineText, GlyphArrangement::addJustifiedText
     */
     void drawText (const String& text,
-                   const Rectangle<int>& area,
+                   Rectangle<int> area,
                    Justification justificationType,
                    bool useEllipsesIfTooBig = true) const;
 
@@ -184,7 +184,7 @@ public:
         @see drawSingleLineText, drawFittedText, drawMultiLineText, GlyphArrangement::addJustifiedText
     */
     void drawText (const String& text,
-                   const Rectangle<float>& area,
+                   Rectangle<float> area,
                    Justification justificationType,
                    bool useEllipsesIfTooBig = true) const;
 
@@ -233,7 +233,7 @@ public:
         @see GlyphArrangement::addFittedText
     */
     void drawFittedText (const String& text,
-                         const Rectangle<int>& area,
+                         Rectangle<int> area,
                          Justification justificationFlags,
                          int maximumNumberOfLines,
                          float minimumHorizontalScale = 0.0f) const;
@@ -257,12 +257,12 @@ public:
     /** Fills a rectangle with the current colour or brush.
         @see drawRect, fillRoundedRectangle
     */
-    void fillRect (const Rectangle<int>& rectangle) const;
+    void fillRect (Rectangle<int> rectangle) const;
 
     /** Fills a rectangle with the current colour or brush.
         @see drawRect, fillRoundedRectangle
     */
-    void fillRect (const Rectangle<float>& rectangle) const;
+    void fillRect (Rectangle<float> rectangle) const;
 
     /** Fills a rectangle with the current colour or brush.
         @see drawRect, fillRoundedRectangle
@@ -297,11 +297,11 @@ public:
     /** Uses the current colour or brush to fill a rectangle with rounded corners.
         @see drawRoundedRectangle, Path::addRoundedRectangle
     */
-    void fillRoundedRectangle (const Rectangle<float>& rectangle,
+    void fillRoundedRectangle (Rectangle<float> rectangle,
                                float cornerSize) const;
 
     /** Fills a rectangle with a checkerboard pattern, alternating between two colours. */
-    void fillCheckerBoard (const Rectangle<int>& area,
+    void fillCheckerBoard (Rectangle<int> area,
                            int checkWidth, int checkHeight,
                            Colour colour1, Colour colour2) const;
 
@@ -321,7 +321,7 @@ public:
         The lines are drawn inside the given rectangle, and greater line thicknesses extend inwards.
         @see fillRect
     */
-    void drawRect (const Rectangle<int>& rectangle, int lineThickness = 1) const;
+    void drawRect (Rectangle<int> rectangle, int lineThickness = 1) const;
 
     /** Draws a rectangular outline, using the current colour or brush.
         The lines are drawn inside the given rectangle, and greater line thicknesses extend inwards.
@@ -338,7 +338,7 @@ public:
     /** Uses the current colour or brush to draw the outline of a rectangle with rounded corners.
         @see fillRoundedRectangle, Path::addRoundedRectangle
     */
-    void drawRoundedRectangle (const Rectangle<float>& rectangle,
+    void drawRoundedRectangle (Rectangle<float> rectangle,
                                float cornerSize, float lineThickness) const;
 
     /** Fills a 1x1 pixel using the current colour or brush.
@@ -358,7 +358,7 @@ public:
         The ellipse is drawn to fit inside the given rectangle.
         @see drawEllipse, Path::addEllipse
     */
-    void fillEllipse (const Rectangle<float>& area) const;
+    void fillEllipse (Rectangle<float> area) const;
 
     /** Draws an elliptical stroke using the current colour or brush.
         @see fillEllipse, Path::addEllipse
@@ -369,7 +369,7 @@ public:
     /** Draws an elliptical stroke using the current colour or brush.
         @see fillEllipse, Path::addEllipse
     */
-    void drawEllipse (const Rectangle<float>& area, float lineThickness) const;
+    void drawEllipse (Rectangle<float> area, float lineThickness) const;
 
     //==============================================================================
     /** Draws a line between two points.
@@ -581,7 +581,7 @@ public:
         method can be used to optimise a component's paint() method, by letting it
         avoid drawing complex objects that aren't within the region being repainted.
     */
-    bool clipRegionIntersects (const Rectangle<int>& area) const;
+    bool clipRegionIntersects (Rectangle<int> area) const;
 
     /** Intersects the current clipping region with another region.
 
@@ -595,7 +595,7 @@ public:
         @returns true if the resulting clipping region is non-zero in size
         @see setOrigin, clipRegionIntersects
     */
-    bool reduceClipRegion (const Rectangle<int>& area);
+    bool reduceClipRegion (Rectangle<int> area);
 
     /** Intersects the current clipping region with a rectangle list region.
 
@@ -625,7 +625,7 @@ public:
     bool reduceClipRegion (const Image& image, const AffineTransform& transform);
 
     /** Excludes a rectangle to stop it being drawn into. */
-    void excludeClipRegion (const Rectangle<int>& rectangleToExclude);
+    void excludeClipRegion (Rectangle<int> rectangleToExclude);
 
     /** Returns true if no drawing can be done because the clip region is zero. */
     bool isClipEmpty() const;