In this paper, we question the idea that large organizations have advantages that make them particularly potent rivals. We argue that the ability of large organizations to ameliorate competitive constraints insulates them from an important source of organizational development and protects them from being selected out if unfit. Consequently, we predict that although large organizations are likely to do well in technology contests, they also are likely to become weak competitors over time compared with small organizations. We specify this prediction in an explicit model of “Red Queen” competition, in which exposure to competition makes organizations both more viable and stronger competitors. We find support for our ideas in empirical estimates of the model obtained using data on hard disk drive manufacturers. Large organizations led the technology race in this market yet failed to develop into stronger competitors through Red Queen competition compared with their small counterparts. We also find evidence that all organizations in this market generated increasingly global competition, regardless of the competitiveness of their home markets. In these ways, our model elucidates important reasons why some organizations are stronger competitors and reveals how strategies that isolate organizations from competition may backfire.