Inventory clearing sales, especially in the case of highly competitive, established products, are sometimes accompanied by temporary discounts in the purchase price, to encourage customers to place orders larger than usual. This paper presents a generalized model of this temporary price discount problem in which explicit recognition is given to widely used variations (i) in the length of the grace period within which prospective buyers may place the discounted order; (ii) in the size of the order needed to qualify for the discounts; and (iii) in the portion of the order eligible for the discount.