  A semigroup is \emph{amiable} if there is exactly one idempotent in each
$\mathcal{R}^*$-class and in each $\mathcal{L}^*$-class. A semigroup is
\emph{adequate} if it is amiable and if its idempotents commute. We
characterize adequate semigroups by showing that they are precisely those
amiable semigroups which do not contain isomorphic copies of two particular
nonadequate semigroups as subsemigroups.
