  We argue that it is possible to maintain both supersymmetry and integrability
in the boundary tricritical Ising field theory. Indeed, we find two sets of
boundary conditions and corresponding boundary perturbations which are both
supersymmetric and integrable. The first set corresponds to a ``direct sum'' of
two non-supersymmetric theories studied earlier by Chim. The second set
corresponds to a one-parameter deformation of another theory studied by Chim.
For both cases, the conserved supersymmetry charges are linear combinations of
Q, \bar Q and the spin-reversal operator \Gamma.
