AD9694 Settling

Hi, I'm running an AD9694 at 400MHz.  I'm testing the settling time with a flat top input.  I see behavior as shown in the attached images - the input to the AD9694 is flat, but the digitized output shows an overshoot and slow settling over a few 100 ns.  Has anyone else tested the AD9694's behavior with square inputs?  Is this intrinsic to the ADC?  The ADC is driven by a fully differential amp, followed by a final filter of a pair of series 50 ohm resistors with a differential 10pF capacitor and two 1pF capacitors to ground.  I'm measuring the input square wave across the 10pF capacitor right before the ADC inputs.  I've tried boosting that capacitor to 100pF.  That slowed down the edges of the square wave, but didn't change the overshoot.