This paper is devoted to the problem of model building from data produced by a nonlinear dynamical system. Unlike most published works that address the problem from a black-box perspective, in the present paper a procedure is developed that permits the use of prior knowledge about the location of fixed-points in addition to the data thus resulting in a gray-box approach. Numerical results using Chua's double-scroll attractor and the sine map are presented. As discussed, the suggested procedure is useful as a means to partially compensate for the loss of information due to noise and to improve dynamical performance in the presence of model structure mismatches. Preliminary results have indicated that the procedure outlined in this paper is a systematic way of searching for models in the vicinity of the black-box solution. This could have important consequences not only in model building but also in model validation.