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We discuss the operation of novel coupled-resonator filters with single-layer acoustic couplers. Our analysis employs the physical Mason model for acoustic resonators. Their simpler fabrication process is counterbalanced by the high acoustic attenuation of suitable coupler materials. At high levels of attenuation, both the phase and the acoustic impedance must be treated as complex quantities to accurately predict the filter insertion loss. We demonstrate that the typically poor near-band rejection of coupled resonator filters can be improved at the die level by connecting a small capacitance between the input and output of the filter to produce a pair of tunable transmission minima. We make use of these theoretical findings to fabricate coupled resonators filters operating at 2.45 GHz.