On the Jung method in positive characteristic

Let (X) over bar be a germ of normal surface with local ring (R) over bar covering a germ of regular surface X with local ring R of characteristic p > 0. Given an extension of valuation rings W/V birationally dominating (R) over bar /R, we study the existence of a new such pair of local rings (R) over bar'/R' birationally dominating (R) over bar /R, such that R' is regular and (R) over bar' has only toric singularities. This is achieved when W/V is defectless or when [W : V] is equal to p.