diff --git a/bundles/org.eclipse.swt/Eclipse SWT PI/cocoa/org/eclipse/swt/internal/cocoa/OS.java b/bundles/org.eclipse.swt/Eclipse SWT PI/cocoa/org/eclipse/swt/internal/cocoa/OS.java
index fffa4837edc..284026717b5 100644
--- a/bundles/org.eclipse.swt/Eclipse SWT PI/cocoa/org/eclipse/swt/internal/cocoa/OS.java	
+++ b/bundles/org.eclipse.swt/Eclipse SWT PI/cocoa/org/eclipse/swt/internal/cocoa/OS.java	
@@ -2179,6 +2179,7 @@ public static Selector getSelector (long value) {
 public static final int NSBackspaceCharacter = 8;
 public static final int NSBevelLineJoinStyle = 2;
 public static final int NSBezelBorder = 2;
+public static final int NSBezelStyleFlexiblePush = 2;
 public static final int NSBoldFontMask = 2;
 public static final int NSBorderlessWindowMask = 0;
 public static final int NSBottomTabsBezelBorder = 2;
diff --git a/bundles/org.eclipse.swt/Eclipse SWT/cocoa/org/eclipse/swt/widgets/Button.java b/bundles/org.eclipse.swt/Eclipse SWT/cocoa/org/eclipse/swt/widgets/Button.java
index 571b793a070..c71f7da62a8 100644
--- a/bundles/org.eclipse.swt/Eclipse SWT/cocoa/org/eclipse/swt/widgets/Button.java	
+++ b/bundles/org.eclipse.swt/Eclipse SWT/cocoa/org/eclipse/swt/widgets/Button.java	
@@ -829,8 +829,11 @@ void setBounds (int x, int y, int width, int height, boolean move, boolean resiz
 		}
 
 		NSButton button = (NSButton)view;
-		if (height > heightThreshold) {
-			button.setBezelStyle(OS.NSRegularSquareBezelStyle);
+		// Use NSBezelStyleFlexiblePush when a custom font is set or when the height
+		// exceeds the standard button height. NSRoundedBezelStyle assumes the macOS
+		// default font size (13pt) and clips text at larger sizes.
+		if (height > heightThreshold || font != null) {
+			button.setBezelStyle(OS.NSBezelStyleFlexiblePush);
 		} else {
 			button.setBezelStyle(OS.NSRoundedBezelStyle);
 		}
@@ -845,10 +848,15 @@ void setBounds (int x, int y, int width, int height, boolean move, boolean resiz
 }
 
 @Override
-void setFont (NSFont font) {
+void setFont (NSFont nsFont) {
 	if (text != null) {
 		((NSButton)view).setAttributedTitle(createString());
 	}
+	if ((style & (SWT.PUSH | SWT.TOGGLE)) != 0 && (style & (SWT.FLAT | SWT.WRAP)) == 0) {
+		// Use NSBezelStyleFlexiblePush when a custom font is set. NSRoundedBezelStyle
+		// assumes the macOS default font size (13pt) and clips text at larger sizes.
+		((NSButton)view).setBezelStyle(font != null ? OS.NSBezelStyleFlexiblePush : OS.NSRoundedBezelStyle);
+	}
 }
 
 @Override
diff --git a/tests/org.eclipse.swt.tests/JUnit Tests/org/eclipse/swt/tests/junit/Test_org_eclipse_swt_widgets_Button.java b/tests/org.eclipse.swt.tests/JUnit Tests/org/eclipse/swt/tests/junit/Test_org_eclipse_swt_widgets_Button.java
index d406cedb87f..df252704b57 100644
--- a/tests/org.eclipse.swt.tests/JUnit Tests/org/eclipse/swt/tests/junit/Test_org_eclipse_swt_widgets_Button.java	
+++ b/tests/org.eclipse.swt.tests/JUnit Tests/org/eclipse/swt/tests/junit/Test_org_eclipse_swt_widgets_Button.java	
@@ -28,8 +28,11 @@
 import org.eclipse.swt.events.SelectionEvent;
 import org.eclipse.swt.events.SelectionListener;
 import org.eclipse.swt.graphics.Color;
+import org.eclipse.swt.graphics.Font;
+import org.eclipse.swt.graphics.FontData;
 import org.eclipse.swt.graphics.Image;
 import org.eclipse.swt.graphics.ImageGcDrawer;
+import org.eclipse.swt.graphics.Point;
 import org.eclipse.swt.layout.FillLayout;
 import org.eclipse.swt.layout.GridLayout;
 import org.eclipse.swt.widgets.Button;
@@ -584,6 +587,34 @@ public void test_consistency_DragDetect () {
 	consistencyEvent(5, 5, 15, 15, ConsistencyUtility.MOUSE_DRAG);
 }
 
+/**
+ * Test that a push button reports a greater preferred height after its font
+ * size is increased. A button whose font grows larger must compute a
+ * proportionally taller preferred size so that layout managers allocate
+ * sufficient space and the text is not clipped.
+ *
+ * @see <a href="https://github.com/eclipse-platform/eclipse.platform.swt/issues/3085">issue #3085</a>
+ */
+@Test
+public void test_computeSize_largerWithLargeCustomFont() {
+	button.setText("OK");
+	shell.open();
+
+	Point defaultSize = button.computeSize(SWT.DEFAULT, SWT.DEFAULT);
+
+	FontData[] fontData = button.getFont().getFontData();
+	Font largeFont = new Font(button.getDisplay(), fontData[0].getName(), 50, fontData[0].getStyle());
+	try {
+		button.setFont(largeFont);
+		SwtTestUtil.processEvents();
+		Point largeSize = button.computeSize(SWT.DEFAULT, SWT.DEFAULT);
+		assertTrue(largeSize.y > defaultSize.y,
+				"Button with 50 pt font should be taller than button with default font");
+	} finally {
+		largeFont.dispose();
+	}
+}
+
 /** Test for Bug 381668 - NPE when disposing radio buttons right before they should gain focus */
 @Disabled(value = "Test works fine locally but fails to get correct focus on automated builds.")
 @Test