Simultaneous MR-PET is an increasingly popular multimodal imaging technique that is able to combine metabolic information obtained from PET with anatomical/functional information from MRI. One of the key technological challenges of the technique is the integration of a PET-transparent MR coil system, a solution to which is demonstrated here for a double-tuned 1H/31P head coil at 3 T. Two single-resonant birdcage coils tuned to the 1H and 31P resonances were arranged in an interleaved fashion and electrically decoupled with the use of trap circuits. All high 511 keV quanta absorbing components were arranged outside the PET field-of-view in order to minimize count rate reduction. The materials inside the PET field-of-view were carefully evaluated and chosen for minimum impact on the PET image quality. As far as possible, the coil case was geometrically optimized to avoid sharp transitions in attenuation, which may potentially result in streaking artefacts during PET image reconstruction. The coil caused a count rate loss of just above 5% when inserted into the PET detector ring. Except for the anterior region, which was designed to maintain free openings for increased patient comfort, an almost uniform distribution of 511 keV attenuation was maintained around the circumference of the coil. MR-related performance for both nuclei was similar or slightly better than that of a commercial double-tuned coil, despite the MR-PET coil having a close-fitting RF screen to shield the PET and MR electronics from possible electromagnetic interferences.