An efficient backtracking method for LISP, used in the MLISP2 language, is described. The method is optimal in the following senses: to the desired goal. At each branching point in the tree, a decision must be made as to which alternative to try next. Backtracking is designed to simplify the programming of this type of problem. <1) Only necessary state information is saved. The backtracking system routines are sufficiently efficient to require less than ten percent of the execution time of typical jobs. (2) Most common operations — fetching/storing the value of a variable or the property of an atom, function entry/exit — take no longer with backtracking than without it. This is