  We study the power of dephasing-covariant operations in the resource theories
of coherence and entanglement. These are quantum operations whose actions
commute with a projective measurement. In the resource theory of coherence, we
find that any two states are asymptotically interconvertible under
dephasing-covariant operations. This provides a rare example of a resource
theory in which asymptotic reversibility can be attained without needing the
maximal set of resource non-generating operations. When extended to the
resource theory of entanglement, the resultant operations share similarities
with LOCC, such as prohibiting the increase of all R\'enyi $\alpha$-entropies
of entanglement under pure state transformations. However, we show these
operations are still strong enough to enable asymptotic reversibility between
any two maximally correlated mixed states, even in the multipartite setting.
