  We study bundles on projective spaces that have vanishing lower cohomologies
using their short minimal free resolutions. We partition the moduli
$\mathbf{M}$ according to the Hilbert function $H$ and classify all possible
Hilbert functions $H$ of such bundles. For each $H$, we describe a
stratification of $\mathbf{M}_H$ by quotients of rational varieties. We show
that the closed strata form a graded lattice given by the Betti numbers.
