Spin injection and detection is achieved in freely suspended graphene using cobalt electrodes and a nonlocal spin-valve geometry. The devices are fabricated with a single electron-beam-resist poly(methyl methacrylate) process that minimizes both the fabrication steps and the number of (aggressive) chemicals used, greatly reducing contamination and increasing the yield of high-quality, mechanically stable devices. As-grown devices can present mobilities exceeding 104 cm2 V−1 s−1 at room temperature and, because the contacts deposited on graphene are only exposed to acetone and isopropanol, the method is compatible with almost any contacting material. Spin accumulation and spin precession are studied in these nonlocal spin valves. Fitting of Hanle spin precession data in bilayer and multilayer graphene yields a spin relaxation time of ∼125-250 ps and a spin diffusion length of 1.7-1.9 μm at room temperature.