  Let $\mathcal F$ be a holomorphic one-dimensional foliation on $\mathbb{P}^n$
such that the components of its singular locus $\Sigma$ are curves $C_i$ and
points $p_j$. We determine the number of $p_j$, counted with multiplicities, in
terms of invariants of $\mathcal F$ and $C_i$, assuming that $\mathcal F$ is
special along the $C_i$. Allowing just one nonzero dimensional component on
$\Sigma$, we also prove results on when the foliation happens to be determined
by its singular locus.
