Character degrees of some $p$-groups

We restrict the possibilities for the character degrees of $p$-groups $G$ satisfying $\mathrm{\mid }G:G^{\mathrm{\prime }}\mathrm{\mid }=p^2$. E.g. if $G$ is of maximal class and has an irreducible character of degree $>p$, then it has such a character of degree at most $p^{\frac{p+1}{2}}$.