Delivery lead-time has become a factor of competitiveness for companies and an important criterion of purchase for the customers today. Thus, in order to increase their profit, companies must not focus only on price but also need to quote the right delivery lead time to their customers. Some authors to find a way in quoting the right delivery lead-time while considering an M/M/1 system. In M/M/1, all customers are accepted. This can lead to longer lead times in the queue. Firms can react by quoting longer lead times in order to cope with this situation. However, this leads to lower demand and revenue. Starting from this observation, we investigate in this paper whether a customer rejection policy can be more beneficial for the firm than an all-customers’ acceptance policy. Indeed, our idea is based on the fact that rejecting some customers might help to quote shorter lead time for the accepted customers, which might lead to higher demand and profit. We model this rejection policy based on an M/M/1/K system. We analytically determine the optimal firm’s policy (optimal price and quoted lead time) in case of M/M/1/1 system. Then, we compare the optimal firm’s profit under M/M/1/1 with the optimal profit obtained by M/M/1. Two situations are considered: a system without holding and penalty costs and a system where these costs are included.