We consider a waveguide composed of two not necessity equal semi-infinite strips (trunks)and a rectangle (resonator)connected by narrow openings in the shared walls.As their diameter vanishes,we construct asymptotics for the scattering coefficients,justifying them by the technique of weighted spaces with detached asymptotics.We establish a criterion for the possibility of observing,at a given frequency, almost complete transmission of waves through both perforated cross-walls.This effect is revealed due to a fine-tuning of the resonator heightand the criterion involves an equationrelating some geometrical characteristics of the waveguideto the wave numbers in the trunks,while any mirror symmetry turns the criterion trivial.