diff --git a/modules/juce_gui_basics/native/juce_mac_NSViewComponentPeer.mm b/modules/juce_gui_basics/native/juce_mac_NSViewComponentPeer.mm
index ba4bfb25e5..8987a60f14 100644
--- a/modules/juce_gui_basics/native/juce_mac_NSViewComponentPeer.mm
+++ b/modules/juce_gui_basics/native/juce_mac_NSViewComponentPeer.mm
@@ -1324,9 +1324,9 @@ public:
         if (auto keyCode = getKeyCodeFromEvent (ev))
         {
             if (isKeyDown)
-                keysCurrentlyDown.addIfNotAlreadyThere (keyCode);
+                keysCurrentlyDown.insert (keyCode);
             else
-                keysCurrentlyDown.removeFirstMatchingValue (keyCode);
+                keysCurrentlyDown.erase (keyCode);
         }
     }
 
@@ -1601,7 +1601,7 @@ public:
     uint32 lastRepaintTime;
 
     static ComponentPeer* currentlyFocusedPeer;
-    static Array<int> keysCurrentlyDown;
+    static std::set<int> keysCurrentlyDown;
     static int insideToFrontCall;
 
     static const SEL dismissModalsSelector;
@@ -2556,20 +2556,25 @@ NSWindow* NSViewComponentPeer::createWindowInstance()
 
 //==============================================================================
 ComponentPeer* NSViewComponentPeer::currentlyFocusedPeer = nullptr;
-Array<int> NSViewComponentPeer::keysCurrentlyDown;
+std::set<int> NSViewComponentPeer::keysCurrentlyDown;
 
 //==============================================================================
 bool KeyPress::isKeyCurrentlyDown (int keyCode)
 {
-    if (NSViewComponentPeer::keysCurrentlyDown.contains (keyCode))
+    const auto isDown = [] (int k)
+    {
+        return NSViewComponentPeer::keysCurrentlyDown.find (k) != NSViewComponentPeer::keysCurrentlyDown.cend();
+    };
+
+    if (isDown (keyCode))
         return true;
 
     if (keyCode >= 'A' && keyCode <= 'Z'
-         && NSViewComponentPeer::keysCurrentlyDown.contains ((int) CharacterFunctions::toLowerCase ((juce_wchar) keyCode)))
+         && isDown ((int) CharacterFunctions::toLowerCase ((juce_wchar) keyCode)))
         return true;
 
     if (keyCode >= 'a' && keyCode <= 'z'
-         && NSViewComponentPeer::keysCurrentlyDown.contains ((int) CharacterFunctions::toUpperCase ((juce_wchar) keyCode)))
+         && isDown ((int) CharacterFunctions::toUpperCase ((juce_wchar) keyCode)))
         return true;
 
     return false;