  For each pair $(e,\sigma)$ of integers satisfying $2e+3\sigma\ge 0$,
$\sigma\leq -2$, and $e+\sigma\equiv 0\pmod{4}$, with four exceptions, we
construct a minimal, simply connected symplectic 4-manifold with Euler
characteristic $e$ and signature $\sigma$. We also produce simply connected,
minimal symplectic 4-manifolds with signature zero (resp. signature -1) with
Euler characteristic $4k$ (resp. $4k+1$) for all $k\ge 46$ (resp. $k\ge 49$).
