Basic indirect response models where drug alters the production (kin) of the response variable (R) based on the Hill function previously assumed one-compartment distribution of the response variable and simple first-order loss (kout) of R. These models were extended using convolution theory to consideration of two-compartment distribution of R and/or polyexponential loss of R. Theoretical equations and methods of data analysis were developed and simulations are provided to demonstrate expected response behavior based on biexponential response dissipation. The inhibition model was applied to our previous data for inhibition of circadian cortisol secretion by prednisolone. The presence of multicompartment response variables and/or polyexponential loss complicates the response patterns and resolution of pharmacologic parameters of indirect response models and requires careful experimental and data analysis approaches in order to properly evaluate such pharmacodynamic responses. The occurrence of these alternative distribution or disposition components does not alter the area under the effect curve (AUCE) which remains identical to the basic models. Model misselection was addressed by testing fittings comparing the basic and new models. Use of the former for these more complex models does not severely perturb the calculated cardinal dynamic parameters. These models may provide improved insights into indirect responses with complexities in distribution or disposition.