I know satanism welcomes indulgence and discourages compulsion. It says compulsions are the result of forbidden pleasures. But it's also in our nature to desire what we cannot have.
I'm not sure where you're getting the idea that "compulsions are the result of forbidden pleasures". The Satanic Bible
is very clear on the difference between "indulgence" and "compulsion". Compulsions come in all sorts of varieties, not necessarily related to socially taboo indulgences or the Law of the Forbidden.
As for how to address and eliminate compulsions, there are lots of different techniques, and their effectiveness largely depends on the individual and the particular nature of the compulsion. Sometimes a Satanic ritual can help purge the mind of compulsive, self-consuming thoughts. Other times it's a matter of gradually trying to reprogram the old compulsive behavior.