I will describe how to constrain the spectrum of local operators and boundary conditions, in two dimensions, using the numerical bootstrap. Even for rational theories, it is hard to construct examples of boundary conditions which break all symmetry except Virasoro, let alone classify them. Yet, as always, the OPE data associated with each conformal boundary condition obeys crossing and unitarity. The ensuing constraints can be organized in a semidefinite program, which allows to explore a multi-dimensional parameter space involving bulk and boundary data. I will show preliminary plots of the bounds one can obtain.