diff --git a/bundles/org.eclipse.swt/Eclipse SWT Browser/win32/org/eclipse/swt/browser/Edge.java b/bundles/org.eclipse.swt/Eclipse SWT Browser/win32/org/eclipse/swt/browser/Edge.java
index 0f5dec79f93..1d83f74be68 100644
--- a/bundles/org.eclipse.swt/Eclipse SWT Browser/win32/org/eclipse/swt/browser/Edge.java	
+++ b/bundles/org.eclipse.swt/Eclipse SWT Browser/win32/org/eclipse/swt/browser/Edge.java	
@@ -222,9 +222,8 @@ static int callAndWait(long[] ppv, ToIntFunction<IUnknown> callable) {
 	ppv[0] = 0;
 	phr[0] = callable.applyAsInt(completion);
 	completion.Release();
-	Display display = Display.getCurrent();
 	while (phr[0] == COM.S_OK && ppv[0] == 0) {
-		if (!display.readAndDispatch()) display.sleep();
+		processNextOSMessage();
 	}
 	return phr[0];
 }
@@ -241,13 +240,33 @@ static int callAndWait(String[] pstr, ToIntFunction<IUnknown> callable) {
 	pstr[0] = null;
 	phr[0] = callable.applyAsInt(completion);
 	completion.Release();
-	Display display = Display.getCurrent();
 	while (phr[0] == COM.S_OK && pstr[0] == null) {
-		if (!display.readAndDispatch()) display.sleep();
+		processNextOSMessage();
 	}
 	return phr[0];
 }
 
+/**
+ * Processes a single OS message using {@link Display#readAndDispatch()}. This
+ * is required for processing the OS events during browser initialization, since
+ * Edge browser initialization happens asynchronously.
+ * <p>
+ * {@link Display#readAndDisplay()} also processes events scheduled for
+ * asynchronous execution via {@link Display#asyncExec(Runnable)}. This may
+ * include events such as the disposal of the browser's parent composite, which
+ * leads to a failure in browser initialization if processed in between the OS
+ * events for initialization. Thus, this method does not implement an ordinary
+ * readAndDispatch loop, but waits for an OS event to be processed.
+ */
+private static void processNextOSMessage() {
+	Display display = Display.getCurrent();
+	MSG msg = new MSG();
+	while (!OS.PeekMessage (msg, 0, 0, 0, OS.PM_NOREMOVE)) {
+		display.sleep();
+	}
+	display.readAndDispatch();
+}
+
 static ICoreWebView2CookieManager getCookieManager() {
 	if (Instances.isEmpty()) {
 		SWT.error(SWT.ERROR_NOT_IMPLEMENTED, null, " [WebView2: cookie access requires a Browser instance]");
diff --git a/tests/org.eclipse.swt.tests/JUnit Tests/org/eclipse/swt/tests/junit/Test_org_eclipse_swt_browser_Browser.java b/tests/org.eclipse.swt.tests/JUnit Tests/org/eclipse/swt/tests/junit/Test_org_eclipse_swt_browser_Browser.java
index 6c88a2af863..6eb42e4b435 100644
--- a/tests/org.eclipse.swt.tests/JUnit Tests/org/eclipse/swt/tests/junit/Test_org_eclipse_swt_browser_Browser.java	
+++ b/tests/org.eclipse.swt.tests/JUnit Tests/org/eclipse/swt/tests/junit/Test_org_eclipse_swt_browser_Browser.java	
@@ -268,6 +268,17 @@ public void test_ConstructorLorg_eclipse_swt_widgets_CompositeI() {
 	browser = createBrowser(null, SWT.NONE); // Should throw.
 }
 
+/**
+ * Regression test for issue #339: [Edge] No more handle exceptions from Edge browser
+ */
+@Test
+public void test_Constructor_asyncParentDisposal() {
+	Display.getCurrent().asyncExec(() -> {
+		shell.dispose();
+	});
+	Browser browser = createBrowser(shell, SWT.EDGE);
+	assertFalse(browser.isDisposed());
+}
 
 @Test
 public void test_evalute_Cookies () {