We compare in this paper two classes of sequential scoring rules: the first class eliminates at each step the candidate with the lowest score whereas the second one eliminates the candidates whose scores are equal to or lower than the average score of the candidates remaining in contention. We show that, in three-candidate elections, the second method is susceptible to improve the ability of the sequential scoring rules to avoid monotonicity paradoxes, but this benefit is offset by a decrease in the Condorcet efficiency of these rules.