This paper extends the scope and optimality of previous algorithmic debugging techniques of Prolog programs using slicing techniques. We provide a dynamic slicing algorithm (called Debug slice) which augments the data flow analysis with control-flow dependences in order to identify the source of a bug included in a program. We developed a tool for debugging Prolog programs which also handles the specific programming techniques (cut, if-then, OR). This approach combines the Debug slice with Shapiro's algorithmic debugging technique.