  The Colless index is one of the oldest and most widely used balance indices
for rooted bifurcating trees. Despite its popularity, its minimum value on the
space $\mathcal{T}_n$ of rooted bifurcating trees with $n$ leaves is only known
when $n$ is a power of 2. In this paper we fill this gap in the literature, by
providing a formula that computes, for each $n$, the minimum Colless index on
$\mathcal{T}_n$, and characterizing those trees where this minimum value is
reached.
