We utilize nanoscale spin valves with Pt spacer layers to characterize spin relaxation in Pt. Analysis of the spin lifetime indicates that Elliott-Yafet spin scattering is dominant at room temperature, but an unexpected intrinsic Dyakonov-Perel-like spin relaxation becomes dominant at cryogenic temperatures. We also observe suppression of spin relaxation in a Pt layer interfaced with a ferromagnet, likely caused by the competition between the effective exchange and spin-orbit fields.