This paper presents a new algorithm for efficiently generating the minimal cut-sets of a fault tree containing repetitions of basic events. The algorithm is easily performed by hand and substantially reduces both execution time and storage requirements, over the classical technique, when programmed. The savings are accomplished by recognizing and recursively reducing the influence of the repetitive events. The theoretical basis of the algorithm is presented and examples from the recent literature, used to demonstrate its efficiency. Finally, the computational complexity is discussed and rules presented for simplifying the tree before the computations begin.