In many real-world multiobjective optimization problems one needs to find solutions or alternatives that provide a fair compromise between different conflicting objective functions--which could be criteria in a multicriteria context, or agent utilities in a multiagent context--while being efficient (i.e. informally, ensuring the greatest possible overall agents' satisfaction). This is typically the case in problems implying human agents, where fairness and efficiency requirements must be met. Preference handling, resource allocation problems are another examples of the need for balanced compromises between several conflicting objectives. A way to characterize good solutions in such problems is to use the leximin preorder to compare the vectors of objective values, and to select the solutions which maximize this preorder. In this article, we describe five algorithms for finding leximin-optimal solutions using constraint programming. Three of these algorithms are original. Other ones are adapted, in constraint programming settings, from existing works. The algorithms are compared experimentally on three benchmark problems.