We integrate field data and phylogenetic comparative analyses to investigate causes of body size evolution and stasis in an old insect order: odonates (“dragonflies and damselflies”). Fossil evidence for “Cope's Rule” in odonates is weak or non-existent since the last major extinction event 65 million years ago, yet selection studies show consistent positive selection for increased body size among adults. In particular, we find that large males in natural populations of the banded demoiselle (Calopteryx splendens) over several generations have consistent fitness benefits both in terms of survival and mating success. Additionally, there was no evidence for stabilizing or conflicting selection between fitness components within the adult life-stage. This lack of stabilizing selection during the adult life-stage was independently supported by a literature survey on different male and female fitness components from several odonate species. We did detect several significant body size shifts among extant taxa using comparative methods and a large new molecular phylogeny for odonates . We suggest that the lack of Cope's rule in odonates results from conflicting selection between fitness advantages of large adult size and costs of long larval development. We also discuss competing explanations for body size stasis in this insect group.