This paper presents a new model and an efficient solution algorithm for a bi-objective one-dimensional trim-loss problem. In the trim-loss – or cutting-stock – problem, customer orders of different smaller item sizes are satisfied by cutting a number of larger standard-size objects. After cutting larger objects to satisfy orders for smaller items, the remaining parts are considered as useless or wasted material, which is called “trim-loss”. The two objectives of the proposed model, in the order of priority, are to minimize: the total trim loss, and the number of partially-cut large objects. To produce near-optimum solutions, a two-stage least-loss algorithm (LLA) is used to determine the combinations of small item sizes that minimize the trim loss quantity. Solving several benchmark problems from the literature, the algorithm demonstrated considerable effectiveness in terms of both objectives, in addition to high computational efficiency.