Well after 50 years since the discovery of QCD, we are still lacking a description of the theory of strong interactions at low energies. For instance, we do not know how to produce the rich meson spectrum out of the handful of parameters in the QCD Lagrangian, other than by brute-force lattice simulations. This has prompted a revival of the S-matrix bootstrap, which aims to single out the theory as the unique set of scattering amplitudes consistent with certain self-consistency conditions. This approach has led to sharp, rigorous bounds for pion scattering in the large N limit. But these bounds are completely agnostic about the UV completion of the theory. In this talk I will explain how, by enlarging the system to include form factors and two-point functions, one can input UV information (computed with perturbative QCD) into the bootstrap. We will see how this improves upon the previous bounds.