N280Z

I just replaced the master cylinder on my 280Z but the same problem continues. I have a good firm pedal with the car not running but when I start the engine the pedal goes down another couple of inches but not quite to the floor. The brakes do work but I am concerned about being that close to the end of the pedal travel. It does not help much to pump the pedal. I believe I have bled the system correctly in the right order including bench bleeding the master. The master is new, not rebuilt. I would guess that their is a problem with the booster but I can't understand how the pedal can be good without vaccum and then change. Any ideas would be appreciated. Thanks