The reconstruction of artifact-free images from radially encoded MRI acquisitions poses a difficult task for undersampled data sets, that is for a much lower number of spokes in k-space than data samples per spoke. Here, we developed an iterative reconstruction method for undersampled radial MRI which (i) is based on a nonlinear optimization, (ii) allows for the incorporation of prior knowledge with use of penalty functions, and (iii) deals with data from multiple coils. The procedure arises as a two-step mechanism which first estimates the coil profiles and then renders a final image that complies with the actual observations. Prior knowledge is introduced by penalizing edges in coil profiles and by a total variation constraint for the final image. The latter condition leads to an effective suppression of undersampling (streaking) artifacts and further adds a certain degree of denoising. Apart from simulations, experimental results for a radial spin-echo MRI sequence are presented for phantoms and human brain in vivo at 2.9 T using 24, 48, and 96 spokes with 256 data samples. In comparison to conventional reconstructions (regridding) the proposed method yielded visually improved image quality in all cases. Magn Reson Med 57:1086–1098, 2007. © 2007 Wiley-Liss, Inc.