Future space-borne cloud profiling radars (CPR) will employ longer pulse lengths than ground-based systems. As a consequence, reflectivity profiles observed from space will be more strongly convoluted with the radar pulse shape. Here we describe a constrained linear inverse technique that reduces the effects of this convolution. We apply the technique to simulated data, based on actual observations from the ground, and show that significant improvements in the reflectivity profile can be obtained. Average Z errors (dBz) are halved, while cloud boundaries are substantially better retrieved. The results in this paper are relevant to space-borne missions like CloudSat and EarthCARE. © 2004 Elsevier B.V. All rights reserved.