We derive expressions for the damping rate for a two-level atom trapped in the antinodes of an optical interference pattern. We find that the decay rate is much slower than the rate for untrapped atoms in optical molasses. Although the velocity of untrapped atoms decays exponentially in time, the velocity of trapped atoms decays only as t-1/2. We show that the slow damping rate can be circumvented by the addition of a traveling-wave component to the molasses standing wave and discuss how these results can be extended to multilevel atoms.