  Let $\mathcal{O}$ be the ring of integers of a finite extension of
$\mathbb{Q}_p$. We prove two control theorems for fine Selmer groups of general
cofinitely generated modules over $\mathcal{O}$. We apply these control
theorems to compare the fine Selmer group attached to a modular form $f$ over
the cyclotomic $\mathbb{Z}_p$-extension of $\mathbb{Q}$ to its counterpart
attached to the conjugate modular form $\overline{f}$.
