During the last 25 years there has been a great interest in deriving aquifer characteristics from outflow data. This analysis has been mainly based of the drainage of a horizontal aquifer after sudden drawdown, using the Boussinesq approximation. Following the general approach of Brutsaert and Lopez [Brutsaert W, Lopez, JP. Basin-scale geohydrologic drought flow features of riparian aquifers in the southern Great Plains. Water Resour Res 1998;34(2):233–40], it was determined that for this geometry the aquifer behavior could be characterized by dQ/dt∝Q3 for small t and by dQ/dt∝Q3/2 for large t. It was remarked that dQ/dt∝Q for large t is often observed. In practice, it is also difficult to determine if dQ/dt∝Q3 for small t because this behavior can only be observed over a very short period.Here, we present a similar analysis of aquifer behavior based on the more fundamental Laplace solution for penetrated aquifers. It has been shown that also when the drain does not fully penetrate the aquifer, the solution still produces good results [Szilagyi, J. Sensitivity analysis of aquifer parameter estimations based on the Laplace equation with linearized boundary conditions. Water Resour Res 2003;39(6)]. The Laplace solution quickly shows that dQ/dt∝Q for t→∞ and dQ/dt∝Q∞ for t→0, after sudden drawdown. This analysis reconfirms previous findings concerning long-time behavior. More importantly, the analysis shows that the exponent B in dQ/dt∝QB does not have a fixed limited value for short times for the given geometry. Further analysis, however, shows that under certain conditions the relation dQ/dt∝Q3 is retained for 0≪t