A new concept is proposed for the full-wave computer-aided design of microwave filters. The method consists of two stages and operates on the zeros and poles of the transfer function and their derivatives. These quantities are evaluated from the response computed by a full-wave electromagnetic solver with two levels of accuracy. The two stages make use of different models that are optimized using a low-accuracy electromagnetic solver. The design involves one coarse-level optimization in the first stage and a few iterations in the second stage, each requiring a single computation of a high-accuracy response. The effectiveness of the proposed technique is demonstrated with two examples, in which design closure was achieved with just three evaluations of the high-accuracy full-wave solutions irrespective of the quality of the initial design.