Where is tree-level string theory?

We investigate the space of consistent tree-level extensions of the maximal supergravities in ten dimensions. We parametrize theory space by the first few EFT coefficients and by the on-shell coupling of the lightest massive state, and impose on these data the constraints that follow from 2 -> 2 supergraviton scattering. While Type II string theory lives strictly inside the allowed region, we uncover a novel extremal solution of the bootstrap problem, which appears to contain a single linear Regge trajectory, with the same slope as string theory. We repeat a similar analysis for supergluon scattering, where we find instead a continuous family of extremal solutions with a single Regge trajectory of varying slope.