A550 built-in flash overexposure.

I set my A550 in tripod. Central focus point, single auto focus. Shoot the same subject, keep the same ISO. When I use Program mode the exposure with the pop-up flash is good. I notice the speed and the aperture the camera has selected. I use the same aperture in Aperture priority mode. The A550 naturally selects the speed it had selected in Program mode. Now with the pop-up flash it overexposes badly. I have repeatedly tested with ADI, no ADI simple TTL, matrix metering or spot metering. Always the same problem: with a certain speed and aperture in Program mode on built-in flash exposures acceptably, the same speed and aperture in Aperture mode on built-in flash terribly over exposures. Am I missing something? What can I do to make my A550 exposure correctly in every mode with the built-in flash?

By the way, I have an external Metz that never gave me such problems.