Realistic environmental models used for decision making typically require a highly parameterized approach. Calibration of such models is computationally intensive because widely used parameter estimation approaches require individual forward runs for each parameter adjusted. These runs construct a parameter-to-observation sensitivity, or Jacobian, matrix used to develop candidate parameter upgrades. Parameter estimation algorithms are also commonly adversely affected by numerical noise in the calculated sensitivities within the Jacobian matrix, which can result in unnecessary parameter estimation iterations and less model-to-measurement fit. Ideally, approaches to reduce the computational burden of parameter estimation will also increase the signal-to-noise ratio related to observations influential to the parameter estimation even as the number of forward runs decrease. In this work a simultaneous increments, an iterative ensemble smoother (IES), and a randomized Jacobian approach were compared to a traditional approach that uses a full Jacobian matrix. All approaches were applied to the same model developed for decision making in the Mississippi Alluvial Plain, USA. Both the IES and randomized Jacobian approach achieved a desirable fit and similar parameter fields in many fewer forward runs than the traditional approach; in both cases the fit was obtained in fewer runs than the number of adjustable parameters. The simultaneous increments approach did not perform as well as the other methods due to inability to overcome suboptimal dropping of parameter sensitivities. This work indicates that use of highly efficient algorithms can greatly speed parameter estimation, which in turn increases calibration vetting and utility of realistic models used for decision making.