  We show that the conformally invariant boundary conditions for the
three-state Potts model are exhausted by the eight known solutions. Their
structure is seen to be similar to the one in a free field theory that leads to
the existence of D-branes in string theory. Specifically, the fixed and mixed
boundary conditions correspond to Neumann conditions, while the free boundary
condition and the new one recently found by Affleck et al [1] have a natural
interpretation as Dirichlet conditions for a higher-spin current. The latter
two conditions are governed by the Lee\hy Yang fusion rules. These results can
be generalized to an infinite series of non-diagonal minimal models, and
beyond.
