Experiments were performed to measure the rebound velocities of small plastic and metal spheres dropped from various heights onto a smooth quartz surface coated with a thin layer of viscous fluid. The spheres stick without rebounding for low impact velocities, due to viscous dissipation in the thin fluid layer. Above a critical impact velocity, however, the lubrication forces in the thin layer cause elastic deformation and rebound of the spheres. The apparent coefficient of restitution increases with the ratio of the Stokes number to its critical value for rebound, where the Stokes number is a dimensionless ratio of the inertia of the sphere to viscous forces in the fluid. The critical Stokes number required for rebound decreases weakly with increasing values of a dimensionless elasticity parameter which is a ratio of the viscous forces which cause deformation to the elastic forces which resist deformation. The experimental results show good agreement with an approximate model based on lubrication theory for undeformed spheres and scaling relations for elastic deformation.