If Xt is a Hunt process and T = inf{t>0: (Xt−,Xt)∃KxL,X t− ≠ Xt}, the distribution of X(T) can be determined from a cone of functions calculable from the potential of X and the Levy system of X. The method involves studying the time change Yt of Xt by the inverse of a discontinuous additive functional. We complete Weidenfeld's study of time changing Xt by the inverse of Ct by showing that Yt (restricted to its nonbranch points) is a right process if Xt is a “right semiregenerative process” on \(M \cup \prod = \hat {\rm M}\) where: (1) ¯M is the closed support of Ct, M is the minimal right closed set with closure ¯M, and π=⋆:Ct-Ct}->0. (2) ¯M is homogeneous. (3) Ct is additive on \(\hat M \cup [0]\)