  We study the Selmer group associated to a $p$-ordinary newform $f \in
S_{2r}(\Gamma_0(N))$ over the anticyclotomic $\mathbb{Z}_p$-extension of an
imaginary quadratic field $K/\mathbb{Q}$. Under certain assumptions, we prove
that this Selmer group has no proper $\Lambda$-submodules of finite index. This
generalizes work of Bertolini in the elliptic curve case. We also offer both a
correction and an improvement to an earlier result on Iwasawa invariants of
congruent modular forms by the present authors.
