Contractive projections in Paley-Wiener spaces

Let $S_1$ and $S_2$ be disjoint finite unions of parallelepipeds. We describe necessary and sufficient conditions on the sets $S_1,S_2$ and exponents $p$ such that the canonical projection $P$ from $P{W}_{S_1\cup S_2}^p$ to $P{W}_{S_1}^p$ is a contraction.