  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
rho meson are constructed and can be used as a viable alternative to existing
models.
