Firms consider a variety of factors when making lead-time promises, including current shop status and the size of the incoming order. The profit-maximising model presented in this paper is the first to include reputation effects explicitly in a lend-time optimisation model. Reputation is considered to be the lasting effect on the market of a firm's delivery performance over time, and so it affects the future as well as the current profits. The model is complicated, and a counter-example demonstrates that qualitative monotonicity results are not obtainable. A computational study explores the relationships between shop status, order size, reputation, market characteristics and the lead-time decision. Regression analysis sheds light on these relationships and suggests three heuristics, which provide near-optimal solutions with relatively short running times.