We present an approach to find optimal reflector shapes for non-tracking solar collectors under practical constraints. We focus on cylindrical absorbers and reflectors with translational symmetry. Under idealized circumstances, edge ray reflectors are well known to be optimal. However, it is not clear how optimal reflectors should be shaped in order to obtain maximum utilizable energy for given operating temperatures under practical constraints like reflectivity less than unity, real radiation data, size limits, and gaps between the reflector and the absorber. For a prototype collector with a symmetric edge ray reflector and a tubular absorber, ae derive from calorimetric measurements under outdoor conditions the optical efficiency as a function of the incidence angle. Using numerical optimization and raytracing, we compare truncated symmetric edge ray reflectors; truncated asymmetric edge ray reflectors and free forms parametrized by Bezier splines. We find that asymmetric edge ray reflectors are optimal. For reasonable operating conditions, truncated asymmetric edge ray reflectors allow much better land use and easily adapt to a large range of roof tilt angles with marginal changes in collector construction. Except near the equator, they should increase the yearly utilizable energy per absorber tube by several percent as compared to the prototype collector with symmetric reflectors. (C) 2000 Elsevier Science Ltd. All rights reserved.