Ice in both terrestrial and planetary settings often contains rock particles. Here we present an experimental investigation of the influence of intergranular particles on the rheological behavior of ice. Experiments were performed on samples fabricated from 10‐μm ice powders +1‐μm graphite or 0.8‐μm alumina particles and subjected to elevated confining pressures. A critical particle fraction, ∼6%, was observed, below which samples behave like pure ice and deform by both grain boundary sliding (GBS) and dislocation creep, and above which GBS creep is impeded. Above this critical fraction, ice grains occur in particle‐free clusters surrounded by bands of particles mixed with fine‐grained ice, resulting in the impedance of GBS in the bands as well as sliding between the ice clusters. Our results imply that South Polar Layered Deposits and midlatitude lobate debris aprons on Mars must contain >94% ice and that the shallow subsurface of Ceres could contain >90% ice.