The Brutsaert and Nieber (1977) analysis is a well-known method that can estimate soil parameters given discharge data for some aquifers. It has been used for several cases where the observed late-time behavior of the recession suggests that the water stream that is adjacent to the aquifer has nonzero depth. However, its mathematical formulation is, strictly speaking, not capable of reproducing these real-case scenarios since the early time behavior is based on a solution for which the aquifer stream has zero depth (Polubarinova-Kochina, 1962). We propose a simple generalization for the Brutsaert and Nieber (1977) method that takes into consideration the depth of the adjacent water stream. The generalization is based on already available solutions by Polubarinova-Kochina (1962), Chor et al. (2013) and Dias et al. (2014) and can be readily implemented with little effort. The original and proposed equations are tested against numerical simulations of the full nonlinear Boussinesq equation. A sensitivity analysis shows that the modification can have significant impact on the predicted values of both the drainable porosity and the saturated hydraulic conductivity.