Deploying web service (WS) compositions following a choreography has been attracting considerable interest as it brings the advantages of decentralization in terms of performance and privacy preservation. However, in the absence of a central entity, the choreography model suffers from lack of control regarding the selection of appropriate WSes. This is further aggravated in the case of constrained compositions, where service selection is bounded by a set of requirements imposed either by the user requesting the composite service or by the WSes involved in the composition. In this scenario, it is essential to provide assurance that all selected services satisfied the posed constraints. This requirement might constitute a serious limitation to the acceptance of the choreography model, compared to the central orchestration driven one, as entities might collude to select each other even if they are not enough qualified for the task. To save the benefits of the choreography model all while ensuring control against collusion, we suggest an audit-based correctness control combined with a reputation system. Our approach detects anomalous behaviors, it deters entities from collusion with a punish-based reputation system, and it ensures the audit in a privacy preserving manner without subverting the performance of the choreography approach.