  We determine the stable reduction at $p$ of all three point covers of the
projective line with Galois group ${\rm SL}_2(p)$. As a special case, we
recover the results of Deligne and Rapoport on the reduction of the modular
curves $X_0(p)$ and $X_1(p)$. Our method does not use the fact that modular
curves are moduli spaces. Instead, we rely on results of Raynaud and the
authors which describe the stable reduction of three point covers whose Galois
group is strictly divisible by $p$.
