diff --git a/extras/Demo/Source/Demos/AudioLiveScrollingDisplay.h b/extras/Demo/Source/Demos/AudioLiveScrollingDisplay.h
index efc704466f..ef9e87772c 100644
--- a/extras/Demo/Source/Demos/AudioLiveScrollingDisplay.h
+++ b/extras/Demo/Source/Demos/AudioLiveScrollingDisplay.h
@@ -99,6 +99,7 @@ private:
         int samplesAgo = (nextSample + numElementsInArray (samples) - 1);
 
         RectangleList<float> waveform;
+        waveform.ensureStorageAllocated ((int) numElementsInArray (samples));
 
         for (int x = jmin (getWidth(), (int) numElementsInArray (samples)); --x >= 0;)
         {
diff --git a/extras/Demo/Source/Demos/GraphicsDemo.cpp b/extras/Demo/Source/Demos/GraphicsDemo.cpp
index 8e20d1f2f5..07a631b230 100644
--- a/extras/Demo/Source/Demos/GraphicsDemo.cpp
+++ b/extras/Demo/Source/Demos/GraphicsDemo.cpp
@@ -508,6 +508,8 @@ public:
     {
         {
             RectangleList<float> verticalLines;
+            verticalLines.ensureStorageAllocated (getWidth());
+
             float pos = offset.getValue();
 
             for (int x = 0; x < getWidth(); ++x)
@@ -523,6 +525,8 @@ public:
 
         {
             RectangleList<float> horizontalLines;
+            horizontalLines.ensureStorageAllocated (getHeight());
+
             float pos = offset.getValue();
 
             for (int y = 0; y < getHeight(); ++y)
diff --git a/modules/juce_audio_utils/gui/juce_AudioThumbnail.cpp b/modules/juce_audio_utils/gui/juce_AudioThumbnail.cpp
index f5cf5d6c6a..3a155b07d6 100644
--- a/modules/juce_audio_utils/gui/juce_AudioThumbnail.cpp
+++ b/modules/juce_audio_utils/gui/juce_AudioThumbnail.cpp
@@ -391,6 +391,7 @@ public:
                 const MinMaxValue* cacheData = getData (channelNum, clip.getX() - area.getX());
 
                 RectangleList<float> waveform;
+                waveform.ensureStorageAllocated (clip.getWidth());
 
                 float x = (float) clip.getX();
 
diff --git a/modules/juce_graphics/geometry/juce_RectangleList.h b/modules/juce_graphics/geometry/juce_RectangleList.h
index 3637f6ad11..f1b81a74ac 100644
--- a/modules/juce_graphics/geometry/juce_RectangleList.h
+++ b/modules/juce_graphics/geometry/juce_RectangleList.h
@@ -628,6 +628,17 @@ public:
     /** Standard method for iterating the rectangles in the list. */
     const RectangleType* end() const noexcept       { return rects.end(); }
 
+    /** Increases the internal storage to hold a minimum number of rectangles.
+        Calling this before adding a large number of rectangles means that
+        the array won't have to keep dynamically resizing itself as the elements
+        are added, and it'll therefore be more efficient.
+        @see Array::ensureStorageAllocated
+    */
+    void ensureStorageAllocated (int minNumRectangles)
+    {
+        rects.ensureStorageAllocated (minNumRectangles);
+    }
+
 private:
     //==============================================================================
     Array<RectangleType> rects;
diff --git a/modules/juce_gui_basics/native/juce_mac_NSViewComponentPeer.mm b/modules/juce_gui_basics/native/juce_mac_NSViewComponentPeer.mm
index 31fc932456..32f1c26576 100644
--- a/modules/juce_gui_basics/native/juce_mac_NSViewComponentPeer.mm
+++ b/modules/juce_gui_basics/native/juce_mac_NSViewComponentPeer.mm
@@ -1222,6 +1222,8 @@ private:
         const Rectangle<int> clipBounds (clipW, clipH);
         const CGFloat viewH = [view frame].size.height;
 
+        clip.ensureStorageAllocated ((int) numRects);
+
         for (int i = 0; i < numRects; ++i)
             clip.addWithoutMerging (clipBounds.getIntersection (Rectangle<int> (roundToInt (rects[i].origin.x) + offset.x,
                                                                                 roundToInt (viewH - (rects[i].origin.y + rects[i].size.height)) + offset.y,