We present a framework for the acquisition of sentential paraphrases based on crowdsourcing. The proposed method maximizes the lexical divergence between an original sentence s and its valid paraphrases by running a sequence of paraphrasing jobs carried out by a crowd of non-expert workers. Instead of collecting direct paraphrases of s, at each step of the sequence workers manipulate semantically equivalent reformulations produced in the previous round. We applied this method to paraphrase English sentences extracted from Wikipedia. Our results show that, keeping at each round n the most promising paraphrases (i.e. the more lexically dissimilar from those acquired at round n-1), the monotonic increase of divergence allows to collect good-quality paraphrases in a cost-effective manner.