We analyze the effect of confining rigid and elastic boundaries on the motility of a model dipolar microswimmer. Flexible boundaries are deformed by the velocity field of the swimmer in such a way that the motility of both extensile and contractile swimmers is enhanced. The magnitude of the increase in swimming velocity is controlled by the ratio of the swimmer-advection and elastic time scales, and the dipole moment of the swimmer. We explain our results by considering swimming between inclined rigid boundaries. © 2013 American Physical Society.