CLONE -QMenu exec()'ed on QSystemTrayIcon::Trigger won't disappear (Windows-only)

To reproduce, replace the Window::iconActivated() function in the desktop/systray Qt example with the following code:

////////////////////////////////////////////////
void Window::iconActivated(QSystemTrayIcon::ActivationReason reason)
{
switch (reason)
{
case QSystemTrayIcon::Trigger:

{ QMenu menu; menu.addAction("Test"); menu.exec(QCursor::pos()); }

break;
case QSystemTrayIcon::DoubleClick:
iconComboBox->setCurrentIndex((iconComboBox->currentIndex() + 1)
% iconComboBox->count());
break;
case QSystemTrayIcon::MiddleClick:
showMessage();
break;
default:
;
}
}
////////////////////////////////////////////////

Then left-click on the icon in the system tray. A menu will come up, but clicking anywhere else on the desktop won't make it disappear. Context menus work fine though. This issue happens only on Windows (tested on XP).