Approximative calculations of pump-probe ionization signals induced by short laser pulses are compared to numerically exact calculations performed in first-order perturbation theory. The motivation is to demonstrate that in cases where the wavepacket prepared by the pump pulse does not move over a region where the difference between the potentials of the involved electronic states changes significantly, the computational effort can be reduced dramatically This is of great importance for quantum mechanical simulations of systems with several degrees of freedom.