The Hamiltonian analysis of the beam-beam interaction is extended, for round beams, by including its finite longitudinal extent. For small synchrotron amplitudes resonance strengths are derived that are smaller than those obtained in the impulse approximation. This is a consequence of averaging over the betatron phase during the collision. Results of simulations that reproduce this feature are also presented. More complete simulations, relevant to storage-ring colliders, argue for bunch lengths comparable to the value of the amplitude function ({beta}) at the interaction point.