Impact experiments in Newtonian fluids with a range of viscosities of 10−3to 60 Pa s demonstrate that transient crater volume and shape (depth‐to‐diameter ratio) depend on target viscosity as well as on gravity. Volume is reduced, and depth‐to‐diameter ratio is increased for cratering events in which viscosity plays a dominant role. In addition to being affected by target kinematic viscosity, viscous scaling is most strongly influenced by projectile diameter, less strongly by projectile velocity, and least strongly by gravity. In a planetary context, viscous effects can occur for craters formed by small or slow moving impacting bodies, low planetary surface densities, high surface viscosities, and low gravity values; conditions all likely for certain impacts into the icy satellites of Saturn and Jupiter, especially if liquid mantles were still present beneath solid crusts. Age dating based on crater counts and size‐frequency distributions for these icy bodies may have to be modified to account for the possibility that viscosity‐dominated craters were initially smaller and deeper than their gravity‐controll