Background: Coevolutionary systems like hosts and their parasites are commonly used model systems for evolutionary studies. Inferring the coevolutionary history based on given phylogenies of both groups is often done by employing a set of possible types of events that happened during coevolution. Costs are assigned to the different types of events and a reconstruction of the common history with a minimal sum of event costs is sought.Results: This paper introduces a new algorithm and a corresponding tool called CoRe-PA, that can be used to infer the common history of coevolutionary systems. The proposed method utilizes an event-based concept for reconciliation analyses where the possible events are cospeciations, sortings, duplications, and (host) switches. All known event-based approaches so far assign costs to each type of cophylogenetic events in order to find a cost-minimal reconstruction. CoRe-PA uses a new parameter-adaptive approach, i.e., no costs have to be assigned to the coevolutionary events in advance. Several biological coevolutionary systems that have already been studied intensely in literature are used to show the performance of CoRe-PA.Conclusion: From a biological point of view reasonable cost values for event-based reconciliations can often be estimated only very roughly. CoRe-PA is very useful when it is difficult or impossible to assign exact cost values to different types of coevolutionary events in advance.