  Let $\mathcal{CP}_n$ be the semigroup of partial contraction mappings on
$[n]=\{1,2,\ldots,n\}$ and let $\mathcal{OCP}_n$ and $\mathcal{ORCP}_n$ be its
subsemigroups consisting of all order-preserving and of all order-preserving or
order-reversing, partial contraction mappings, respectively. In this paper we
obtain the rank of the two semigroups, $\mathcal{OCP}_n$ and
$\mathcal{ORCP}_n$, respectively.
