We present a continuation-passing-style (CPS) transformation for some dynamic delimited-control operators, including Felleisen’s control and prompt, that extends a standard call-by-value CPS transformation. Based on this new transformation, we show how Danvy and Filinski’s static delimited-control operators shift and reset simulate dynamic operators, allaying in passing some skepticism in the literature about the existence of such a simulation. The new CPS transformation and simulation use recursive delimited continuations to avoid undelimited control and the overhead it incurs in implementation and reasoning. Keywords delimited control operators; macro expressibility; continuation-passing style (CPS); shift and reset; control and prompt