Three new iterative methods for the solution of the linear least squares problem with bound constraints are presented and their performance analyzed. The first is a modification of a method proposed by Lötstedt, while the two others are characterized by a technique allowing for fast active set changes, resulting in noticeable improvements in the speed with which constraints active at the solution are identified. The numerical efficiency of those algorithms is experimentally studied, with particular emphasis on the dependence on the starting point and the use of preconditioning for ill-conditioned problems.