Prior work suggests that more valuable patents are cited more and this view has become standard in the empirical innovation literature. Using an NPE-derived dataset with patent-specific revenues we find that the relationship of citations to value in fact forms an inverted-U, with fewer citations at the high end of value than in the middle. Since the value of patents is concentrated in those at the high end, this is a challenge to both the empirical literature and the intuition behind it. We attempt to explain this relationship with a simple model of innovation, allowing for both productive and strategic patents. We find evidence of greater use of strategic patents where it would be most expected: among corporations, in fields of rapid development, in more recent patents and where divisional and continuation applications are employed. These findings have important implications for our basic understanding of growth, innovation, and intellectual property policy.