We report measurements of the response of a Kerr-lens mode-locked Ti:sapphire frequency comb to pump power modulation. For each setting of the laser, the comb expands and contracts about a particular fixed point in frequency. We measured this fixed point and found that it is within 8% of our frequency comb's center. In addition, we found that as we shift the comb's center frequency, the fixed point follows to some extent. It follows that modulating the pump power mostly affects the comb's group velocity, i.e., the repetition rate.