Power corrections to exclusive processes are usually calculated using models for twist–four distribution amplitudes (DA) which are based on the leading–order terms in the conformal expansion. In this work we develop a different approach which does not rely on conformal symmetry but is based instead on renormalon analysis. This way we obtain an upper bound for the contributions of higher conformal spin operators, which translates into a bound on the end–point behavior of DA. The existence of such a bound is important for proving factorization theorems. For the two–particle twist–four DA we find in the renormalon model that the conformal expansion converges but it does not converge uniformly near the end points. This means that power corrections to observables which are particularly sensitive to the region where one valence quark is soft, may be underestimated when using the first few terms in the conformal expansion. The renormalon models of twist–four DA of the pion and the ρ meson are constructed and can be used as a viable alternative to existing models.