Reflectors for lighting can be tailored to produce the desired flux maps (illuminance distributions) precisely, from extended light sources, with a calculational procedure called tailored edge-ray designs (TED’s). We generalize the TED procedure, which has so far been developed only for flat sources, to tubular sources within partial-involute reflectors. The governing differential equations for the reflectors are solved analytically. We present specific results for the practical problem of producing uniform far-field illuminance in symmetric two-dimensional luminaires. It is demonstrated that, relative to flat-source TED’s, these new designs can offer increased uniform core regions, more compact reflectors, and better glare control. We offer a comprehensive analysis of the flux map and geometric properties of partial-involute TED’s. Further improvements are possible with hybrid combinations, as we illustrate with several design examples.