let $x$ be a smooth, geometrically irreducible scheme over a finite field of characteristic $p > 0$. with respect to rigid cohomology, $p$-adic coefficient objects on $x$ come in two types: convergent $f$-isocrystals and the subcategory of overconvergent $f$-isocrystals. overconvergent isocrystals are related to $\ell$-adic etale objects ($\ell\neq p$) via companions theory, and as such it is desirable to understand when an isocrystal is overconvergent. we show (under a geometric tameness hypothesis) that a convergent $f$-isocrystal $e$ is overconvergent if and only if its restriction to all smooth curves on $x$ is. the technique reduces to an algebraic setting where we use skeleton sheaves and crystalline companions to compare $e$ to an isocrystal which is patently overconvergent. joint with kiran kedlaya and james upton.