Laursen and Salter (2006) examined the impact of a firm's search strategy for external knowledge on innovative performance. Based on organizational learning and open innovation literature, we extend the model hypothesizing that the search strategy itself is impacted by firm context. That is, both ‘constraints on the application of firm resources’ and the ‘abundance of external knowledge’ have a direct impact on innovative performance and a firm's search strategy in terms of breadth and depth. Based on a survey of Swiss‐based firms, we find that constraints decrease and external knowledge increases innovative performance. Although constraints lead to a broader but shallower search, external knowledge is associated with the breadth and the depth of the search in a U‐shaped relationship. Copyright © 2013 John Wiley & Sons, Ltd.