Model reduction methodologies for the partial differential equations modeling distributed parameter systems constitute an important first step in controller design. A systematic computer-assisted study illustrating the use of two such methodologies (Approximate Inertial Manifolds and the Karhunen-Loeve expansion) in controlling (stabilizing) a nonlinear reaction-diffusion problem is presented. The approximation quality of the models, issues of computational implementation of the reduction procedure, as well as issues of closed-loop stability are addressed.