  We prove that for a so-called sticky process $S$ there exists an equivalent
probability $Q$ and a $Q$-martingale $\tilde{S}$ that is arbitrarily close to
$S$ in $L^p(Q)$ norm. For continuous $S$, $\tilde{S}$ can be chosen arbitrarily
close to $S$ in supremum norm. In the case where $S$ is a local martingale we
may choose $Q$ arbitrarily close to the original probability in the total
variation norm. We provide examples to illustrate the power of our results and
present applications in mathematical finance.
