I don't remember seeing many discussions of dealing with shame in CBT but this is something that can be quite relevant to treating Avoidant PD. There is the option of pinpointing and modifying dysfunctional thoughts that elicit shame and the option of using "shame-attacK exercises" as in REBT. I also like to have the client (gradually) fill me in on whatever it is that they are terribly ashamed of and what the client thinks others would think "if they knew."