After the advantages of methods of feasible directions in an engineering design environment are pointed out, several modifications to the classical scheme are proposed, aimed at improving computational efficiency while preserving convergence properties. First, an abstract algorithm model is set up and a set of sufficient conditions to insure convergence is given. Several modifications are proposed, inspired by difficulties arising in an engineering design environment, and it is shown that the resulting algorithms satisfy the sufficient conditions just mentioned. An integrated-circuit bipolar operational amplifier is optimized in order to show the improvement in computational efficiency that the proposed enhancements can provide.