  The evolution of supersymmetric A-type D-branes under the bulk
renormalization group flow between two different N=2 minimal models is studied.
Using the Landau-Ginzburg description we show that a specific set of branes
decouples from the infrared theory, and we make detailed predictions for the
behavior of the remaining branes. The Landau-Ginzburg picture is then checked
against a direct conformal field theory analysis. In particular we construct a
natural index pairing which is preserved by the RG flow, and show that the
branes that decouple have vanishing index with the surviving branes.
