The purpose of the paper is to illuminate the costs and benefits of crossing firm boundaries in inbound open innovation (OI) by determining the relationships among partner types, knowledge content and performance. The empirical part of the study is based on a survey of OI collaborations answered by R&D managers in 415 Italian, Finnish and Swedish firms. The results show that the depth of collaboration with different partners (academic/consultants, value chain partners, competitors and firms in other industries) is positively related to innovation performance, whereas the number of different partners and size have negative effects. The main result is that the knowledge content of the collaboration moderates the performance outcomes and the negative impact of having too many different kinds of partners. This illustrates how successful firms use selective collaboration strategies characterized by linking explorative and exploitative knowledge content to specific partners, to leverage the benefits and limit the costs of knowledge boundary crossing processes.