This work addresses the problem of expedited design optimization of decomposable compact microwave structures, particularly impedance matching transformers. The approach proposed here exploits structure decomposition and a bottom-up technique where the elementary building blocks of the transformer circuit of interest are first optimized with respect to specifications extracted from a conventional circuit design, and subsequently, the entire circuit is optimized using the previously obtained building-block dimensions as a starting point. The optimization engine for each stage of the process is adjoint-based gradient search embedded in the trust region framework. The bottom-up approach turns out to be critical from the reliability standpoint: As the initial dimensions obtained from the optimized building blocks already result in reasonably good characteristics of the entire circuit, no global search is required to find a satisfactory design. This is in contrast to direct adjoint-based optimization of the entire circuit which leads to a local optimum, which may not satisfy the imposed requirements. At the same time, computational cost of the design process is reduced compared with direct optimization of the entire circuit, because building block optimization is carried out in low-dimensional search spaces and using simpler (i.e., less expensive) electromagnetic models. Our technique is demonstrated using a three-section impedance matching transformer. Copyright (c) 2016 John Wiley & Sons, Ltd.