Summary: We investigate the \((S - 1, S)\) inventory policy under stuttering Poisson demand and generally distributed lead time when the excess demand is lost. We correct results presented in G. J. Feeney and C. C. Sherbrooke’s seminal paper [Manage. Sci., Ser. A 12, 391–411; correction. ibid. 908 (1966; Zbl 0131.18803)] and note that the stationary distribution of units on order for the general compound Poisson demand case is still an open question.