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Let $ℱ$ 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 $ℱ$ and $C_i$, assuming that $ℱ$ 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.