The doorway window approach for the description of time- and frequency-gated spontaneous emission is extended to the case of overlapping pump and gate pulses, provided one can neglect the transient terms decaying with the characteristic time of the gate pulse. All the transient terms decaying with the characteristic time of the pump pulse, on the other hand, are taken into account. Both the sequential and the coherent contributions to the signal are considered. The comparison of the standard doorway-window approximation with the present more general formulation for a curve-crossing model system reveals that the former is valid for pump-pulse durations up to the order of the vibrational period and becomes qualitatively incorrect for longer pump pulses. (C) 2004 Elsevier B.V. All rights reserved.