  A set $P$ of vertices in a graph $G$ is an open packing if no two distinct
vertices in $P$ have a common neighbor. Among all maximal open packings in $G$,
the smallest cardinality is denoted $\rho^{\rm o}_L(G)$ and the largest
cardinality is $\rho^{\rm o}(G)$. There exist graphs for which these two
invariants are arbitrarily far apart. In this paper we begin the investigation
of the class of graphs that have one size of maximal open packings. By
presenting a method of constructing such graphs we show that every graph is the
induced subgraph of a graph in this class. The main result of the paper is a
structural characterization of those $G$ that do not have a cycle of order less
than $15$ and for which $\rho^{\rm o}_L(G)=\rho^{\rm o}(G)$.
