Benedicks and Misiurewicz showed that given a Misiurewicz interval map $f$, there exists an absolutely continuous $f$-invariant probability measure if and only if $\int \log |Df| dx > -\infty$. We shall concentrate on the ``only if" part of this result and discuss two generalisations of it. One is for Misiurewicz exponential maps ($z \mapsto \lambda \exp(z)$ with $\lambda$ such that the orbit of 0 is bounded). The other is for general smooth interval maps: if the critical points are too flat, no acip with positive entropy exists.