We report on a study of the sliding friction of elastomeric surfaces patterned with ridges and channels (and unstructured flat controls), against both smooth and roughened spherical indenters. Against the smooth spherical indenter, all of the structured surfaces have highly reduced sliding friction due to the reduction in actual area of contact. Against roughened spherical indenters, however, the sliding force for structured samples can be up to 50% greater than that of an unstructured flat control. The mechanism of enhanced friction against a rough surface is due to a combination of increased actual area of contact, interlocking between roughness and the surface structure, and attendant dynamic instabilities that dissipate energy.