Authorized priority alerts are permitted to “pop up” on top of a running screensaver in a computer display without suspending operation of the screensaver. A windows manager monitors for priority alerts from applications. If the screensaver is active in the display, the windows manager determines if the alert issuing application and alert type are permitted to breakthrough the screensaver. If so, an alert notification window identifying the content of the alert is generated and displayed in z-order on top of the screensaver, without interrupting the operation of the screensaver displayed underneath. Some notification windows implement security features by displaying only a portion of the content of the corresponding alert or completely obscuring the content of the alert and only notifying of the presence of the alert. An additional security feature requires the user to enter a password in the notification window before the content or type of alert is displayed.