  A dominating set $D$ in a digraph is a set of vertices such that every vertex
is either in $D$ or has an in-neighbour in $D$. A dominating set $D$ of a
digraph is locating-dominating if every vertex not in $D$ has a unique set of
in-neighbours within $D$. The location-domination number $\gamma_L(G)$ of a
digraph $G$ is the smallest size of a locating-dominating set of $G$. We
investigate upper bounds on $\gamma_L(G)$ in terms of the order of $G$. We
characterize those digraphs with location-domination number equal to the order
or the order minus one. Such digraphs always have many twins: vertices with the
same (open or closed) in-neighbourhoods. Thus, we investigate the value of
$\gamma_L(G)$ in the absence of twins and give a general method for
constructing small locating-dominating sets by the means of special dominating
sets. In this way, we show that for every twin-free digraph $G$ of order $n$,
$\gamma_L(G)\leq\frac{4n}{5}$ holds, and there exist twin-free digraphs $G$
with $\gamma_L(G)=\frac{2(n-2)}{3}$. If moreover $G$ is a tournament or is
acyclic, the bound is improved to $\gamma_L(G)\leq\lceil\frac{n}{2}\rceil$,
which is tight in both cases.
