To increase the upper stop-band width of a superconducting spiral filter, a spurious response was suppressed using additional, deliberately lossy, resonators. Their fundamental resonant frequency is equal to the spurious resonance of the main spirals, and their bandwidth is limited, so they introduce very little loss in the main pass band, and therefore retain the benefits of superconductors. Unintended coupling between resonators is mitigated by iterative design. The absorptive resonators are retro-fitted to an existing filter, and being on a separate, low-cost, substrate in a plane parallel to the main filter, require no additional space, incur only a slight additional cost, and because the metal box is unchanged, result in little extra thermal capacity (which prolongs heating and cooling cycles).