We substantially improve in two scenarios the current state-of-the-art modulus of continuity for weak solutions to the $N-$dimensional, two-phase Stefan problem featuring a $p-$degenerate diffusion: for $p=N\geq 3$, we sharpen it to $\boldsymbol{\omega}(r) \approx \exp (-c| \ln r|^{\frac1N})$; for $p>\max\{2,N\}$, we derive an unexpected H\"older modulus. This is a joint work with Ugo Gianazza and Naian Liao.