Abstract We consider scenarios where several agents must aggregate their preferences over a large set of candidates with a combinatorial structure. That is, each candidate is an element of the Cartesian product of the domains of some variables. We assume agents compactly express their preferences over the candidates via soft constraints. We consider a sequential procedure that chooses one candidate by asking the agents to vote on one variable at a time. While some properties of this procedure have been already studied, here we focus on independence of irrelevant alternatives, non-dictatorship, and strategy-proofness. Also, we perform an experimental study that shows that the proposed sequential procedure yields a considerable saving in time with respect to a non-sequential approach, while the winners satisfy the agents just as well, independently of the variable ordering and of the presence of coalitions of agents.