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This paper presents the modeling and optimization of compact microwave bandpass filters whose compactness leads to complex and strong stray coupling paths, thereby making the identification of a simple and sparse coupling topology difficult and even impossible. The strong coupling coefficients needed for a broadband response can also cause an ambiguity in identifying the spatial extent of local resonances. An equivalent circuit, which is extracted directly from Maxwell's equations, is used in optimizing these filters. The filter is represented by its global resonances instead of individual resonators. The extraction of the parameters of the equivalent circuit is carried out in the physical frequency and not in the normalized frequency in order to preserve the physicality of the equivalent circuit, especially for asymmetric responses. The technique is successfully applied to the optimization of second-order suspended stripline bandpass filters with one transmission zero either below or above the passband, as well as fourth-order filters with three transmission zeros. A fourth-order filter with three transmission zeros is fabricated and measured.