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 \( p=N\ge 3 \), we sharpen it to \( \omega(r)\approx\exp(-c|\ln\ r|^{\frac{1}{N}}); \) for \( p \ge \max\{2,N\} \), we derive an unexpected Hölder modulus.