We have previously shown that square arrays of three-dimensional gold helices can serve as compact broadband circular polarizers. Here, we show by heuristic reasoning supported by numerical calculations that the bandwidth of the device can realistically be increased to 1.5 octaves by tapering the gold-helix radius. The tapering also improves the extinction ratio. Depending on the side from which light impinges onto the tapered helices, the polarization conversions are different. Therefore, the structure is either optimal as polarizer or as analyzer. Corresponding structures for the infrared spectral range are fabricated by direct laser writing and gold electroplating.