  We provide evidence for the existence of non-trivial unitary conformal
boundary conditions for a three-dimensional free scalar field, which can be
obtained via a coupling to the m'th unitary diagonal minimal model. For large m
we can demonstrate the existence of the fixed point perturbatively, and for
smaller values we use the numerical conformal bootstrap to obtain a sharp kink
that smoothly matches onto the perturbative predictions. The wider numerical
analysis also yields universal bounds for the spectrum of any other boundary
condition for the free scalar field. A second kink in these bounds hints at a
second class of non-standard boundary conditions, as yet unidentified.
