  We identify a new way to divide the $\delta$-neighborhood of surfaces
$\mathcal{M}\subset\mathbb{R}^3$ into a finitely-overlapping collection of
rectangular boxes $S$. We obtain a sharp $(l^2,L^p)$ decoupling estimate using
this decomposition, for the sharp range of exponents $2\leq p\leq 4$. Our
decoupling inequality leads to new exponential sum estimates where the
frequencies lie on surfaces which do not contain a line.
