A simple mathematical model for the engagement of rough, permeable, grooved wet clutches has been developed and used to determine the effect of various input parameters (applied load, grooved area, and friction material permeability) on engagement. The model includes the effects of surface roughness according to Patir and Cheng (1978), friction material permeability according to Natsumeda and Miyoshi (1994) and Beavars and Joseph (1967), and grooving in the friction material according to a new approximation. The approach reduces the system of Reynolds and force balance equations to a single, first-order differential equation in film thickness and time. A line searching algorithm, exploiting the low computational cost of function evaluations for the new model, is used to find the set of input parameter combinations yielding the same engagement characteristics. This set of design points is presented as an engagement isosurface in the parameter space (F_app, Φˆ, A_red). The isosurface implicitly gives information about engagement time, and it shows regions in which the desired engagement characteristics cannot be achieved. The input parameters are classified as those affecting the transient portion of engagement and those affecting the steady-state portion.