  We demonstrate how negative powers of screenings arise as a nonperturbative
effect within the operator approach to Liouville theory. This explains the
origin of the corresponding poles in the exact Liouville three point function
proposed by Dorn/Otto and $(\hbox{Zamolodchikov})^2$ (DOZZ) and leads to a
consistent extension of the operator approach to arbitrary integer numbers of
screenings of both types. The general Liouville three point function in this
setting is computed without any analytic continuation procedure, and found to
support the DOZZ conjecture. We point out the importance of the concept of free
field expansions with adjustable monodromies - recently advocated by Petersen,
Rasmussen and Yu - in the present context, and show that it provides a unifying
interpretation for two types of previously constructed local observables.
