  A run is a maximal occurrence of a repetition $v$ with a period $p$ such that
$2p \le |v|$. The maximal number of runs in a string of length $n$ was studied
by several authors and it is known to be between $0.944 n$ and $1.029 n$. We
investigate highly periodic runs, in which the shortest period $p$ satisfies
$3p \le |v|$. We show the upper bound $0.5n$ on the maximal number of such runs
in a string of length $n$ and construct a sequence of words for which we obtain
the lower bound $0.406 n$.
