a gradient gibbs measure is the projection to the gradient variables $\eta_b=\phi_y-\phi_x$ of the gibbs measure of the form $$ p(d\phi)=z^{-1}\exp\bigl\{-\beta\sum_{\langle x,y\rangle}v(\phi_y-\phi_x)\bigr\}d\phi, $$ where $v$ is a potential, $\beta$ is the inverse temperature and $d\phi$ is the product lebesgue measure. the simplest example is the (lattice) gaussian free field $v(\eta)={1 \over 2}\kappa\eta^2$. a well known result of funaki and spohn asserts that, for any uniformly-convex $v$, the possible infinite-volume measures of this type are characterized by the {\it tilt}, which is a vector $u\in{\bf r}^d$ such that $e(\eta_b)=u\cdot b$ for any (oriented) edge $b$. i will discuss a simple example for which this result fails once $v$ is sufficiently non-convex thus showing that the conditions of funaki-spohn's theory are generally optimal. the underlying mechanism is an order-disorder phase transition known, e.g., from the context of the $q$-state potts model with sufficiently large $q$. based on joint work with roman koteck\'y.