Many jurisdictions identify margin procyclicality at central counterparties (CCPs) as a potential threat to financial stability. This paper studies the effect of less procyclical margin models on cleared volumes and risk taking in a stylized CCP. It finds that less procyclical margins do not unambiguously improve financial stability, and that the net effect depends on market characteristics (volatility) and CCP member characteristics (risk aversion). A combination of high volatility plus insufficient risk aversion can lead to additional risk taking, creating exposures to the individual participant that cannot be predictably controlled or managed. In turn, this can lead to erosion of confidence in the CCP and motivation for members to flatten out positions or exit. However, as long as the system is outside this special case, which should be avoidable with proper bank regulation, a moderate amount of margin smoothing can actually stimulate trading, helping restore market confidence.