  Given a compact, oriented surface $S$ of finite genus and finitely many
boundary components, we provide examples of finite covers $\tilde{S}$ of $S$
and non-simple closed curves $\gamma$ on $S$ which lifts to simple closed
curves on $\tilde{S}$. In particular, given any positive integer $n\geq 2$, we
construct explicit non-simple closed curves on $S$ which has a simple lift to a
degree $n$ cover of $S$.
