Several comparison-based complexity results have been published recently, including multi-objective optimization. H owever, these results are, in the multiobjective case, quite pessimistic, due to the huge family of fitness function s considered. Combining assumptions on fitness functions and traditional comparison-based assumptions, we get more r ealistic bounds emphasizing the importance of reducing the number of conflicting objectives for reducing the runtime of multiobjective optimization. The approach can in particular predict lower bounds on the computation time, depend ing on the type of requested convergence: pointwise, or to the whole Pareto set. Also, a new (untested yet) algorith m is proposed for approximating the whole Pareto set.