In one-dimensional real and complex dynamics, a map whose post-singular (or post-critical) set is bounded and uniformly repelling is often called a Misiurewicz map. In results hitherto, perturbing a Misiurewicz map is likely to give a (`chaotic') non-hyperbolic map, as per Jakobson's Theorem for unimodal interval maps. This is despite the hyperbolic parameters forming an open, dense set (at least in the interval setting). We shall present some background results and explain why the contrary holds in the complex exponential family z↦λexp(z): Misiurewicz maps are Lebesgue density points for hyperbolic parameters.