Groundwater models estimated during constant-rate pumping can reproduce observed head yet yield different predictions after the pumping rate changes. This study determines when distinct adjustment times for groundwater flux and hydraulic gradient can be estimated and improve prediction of subsequent drawdown and recovery. The Lagging Darcy law (LDL) yields impulse and unit step responses for a leaky aquifer that can be used in continuous-time groundwater models. Four dimensionless groups relate the two adjustment times to leakage time, pumping duration, and observation distance. The analysis spans 2601 combinations and locates conditions where the two times provide independent information and Hantush prediction error exceeds 5% of the initial drawdown range. Separate observation periods estimate parameters, select the pumping response, and evaluate later predictions. The selection rule chose LDL for 39 of 1296 synthetic Hantush hydrographs; the exact 95% binomial interval was 2.15–4.09%. Field applications comprise a constant-rate pumping test at Dewey and a Louisville well field affected by precipitation and Ohio River stage. The selected LDL response reduced recovery RMSE by 81.0% at Dewey and prediction RMSE by 57.5% at Louisville C26, with a moving block bootstrap interval of 45.5–67.3%. Both predictions also had lower RMSE than persistence. Pumping duration and separation of the constitutive times determine when the classical response is adequate and when delayed adjustment materially affects a later groundwater prediction.