  Let f be a modular form of weight 2 and trivial character. Fix also an
imaginary quadratic field K. We use work of Bertolini-Darmon and Vatsal to
study the mu-invariant of the p-adic Selmer group of f over the anticyclotomic
Zp-extension of K. In particular, we verify the mu-part of the main conjecture
in this context. The proof of this result is based on an analysis of
congruences of modular forms, leading to a conjectural quantitative version of
level-lowering (which we verify in the case that Mazur's principle applies).
