We show that one can construct D-branes in parafermionic and WZW theories (
and their orbifolds) which have very natural geometrical interpretations, a
nd yet are not automatically included in the standard Cardy construction of
D-branes in rational conformal field theory. The relation between these th
eories and their T-dual description leads to an analogy between these D-bra
nes and the familiar A-branes and B-branes of N = 2 theories.