  We study the PBW filtration on the Demazure modules $V_{r_{\gamma}}(\lambda)$
associated to reflections $r_{\gamma}$ at positive roots in type $A_n$, long
roots in type $C_n$, short roots in type $B_n$ and positive roots not involving
the simple root $\alpha_{n-1}$ in type $D_n$. In each type, we construct a
normal polytope labelling a basis for the associated graded space
$\operatorname{gr} V_{r_{\gamma}}(\lambda)$ and prove that the annihilating
ideal of $\operatorname{gr} V_{r_{\gamma}}(\lambda)$ is a monomial ideal.
