Atomic scale dissipation is of great interest in nanomechanics and atomic manipulation. We present dissipation measurements with a linearized, ultrasmall amplitude atomic force microscope which is capable of measuring dissipation at chosen, fixed separations. We show that the dynamic dissipation in the noncontact regime is of the order of a few 10-100 meV per cycle. This dissipation is likely due to the motion of a bistable atomic defect in the tip-surface region. In the contact regime we observe dc hysteresis associated with nanoscale plasticity. We find the hysteretic energy loss to be 1 order of magnitude higher for a silicon surface than for copper.