diff --git a/bundles/org.eclipse.swt/Eclipse SWT/gtk/org/eclipse/swt/widgets/Shell.java b/bundles/org.eclipse.swt/Eclipse SWT/gtk/org/eclipse/swt/widgets/Shell.java
index c55f99be603..7957f7e99d9 100644
--- a/bundles/org.eclipse.swt/Eclipse SWT/gtk/org/eclipse/swt/widgets/Shell.java	
+++ b/bundles/org.eclipse.swt/Eclipse SWT/gtk/org/eclipse/swt/widgets/Shell.java	
@@ -2361,8 +2361,10 @@ void resizeBounds (int width, int height, boolean notify) {
 			GDK.gdk_window_resize (enableWindow, width, height);
 		}
 	}
-	int boxWidth = width - 2*border;
-	int boxHeight = height - 2*border;
+	// GTK rejects negative allocations; a shell smaller than its own border must not
+	// leak a negative size into gtk_widget_size_allocate().
+	int boxWidth = Math.max (0, width - 2*border);
+	int boxHeight = Math.max (0, height - 2*border);
 	if ((style & SWT.RESIZE) == 0) {
 		GTK.gtk_widget_set_size_request (vboxHandle, boxWidth, boxHeight);
 	}
diff --git a/tests/org.eclipse.swt.tests/JUnit Tests/org/eclipse/swt/tests/junit/Test_org_eclipse_swt_widgets_Shell.java b/tests/org.eclipse.swt.tests/JUnit Tests/org/eclipse/swt/tests/junit/Test_org_eclipse_swt_widgets_Shell.java
index d16f1e47ae1..bebbe450e8d 100644
--- a/tests/org.eclipse.swt.tests/JUnit Tests/org/eclipse/swt/tests/junit/Test_org_eclipse_swt_widgets_Shell.java	
+++ b/tests/org.eclipse.swt.tests/JUnit Tests/org/eclipse/swt/tests/junit/Test_org_eclipse_swt_widgets_Shell.java	
@@ -1054,4 +1054,24 @@ public void test_setLocationII() {
 	}
 	super.test_setLocationII();
 }
+
+@Test
+public void test_degenerateSizeDoesNotExpandShell() {
+	// A bordered popup asked for a height of 0 used to be allocated -1, which GTK rejects,
+	// so it fell back to its natural size with its content never laid out. See issue 3539.
+	// GTK4 backs these shells with a GtkPopover, which never went through that box maths
+	// and enforces a minimum height of its own.
+	assumeTrue(SwtTestUtil.isGTK && !SwtTestUtil.isGTK4());
+	Shell popup = new Shell(shell, SWT.TOOL | SWT.ON_TOP);
+	popup.setLayout(new FillLayout());
+	Button child = new Button(popup, SWT.PUSH);
+	child.setText("some content that is clearly taller than two pixels");
+	popup.setSize(228, 0);
+	popup.setVisible(true);
+	SwtTestUtil.processEvents();
+	Rectangle clientArea = popup.getClientArea();
+	popup.dispose();
+	assertTrue(clientArea.height >= 0, "negative client area: " + clientArea);
+	assertTrue(clientArea.height <= 2, "shell expanded to its natural size: " + clientArea);
+}
 }