Most reductionist accounts of intentional joint action include a condition that it must be common knowledge between participants that they have certain intentions and beliefs that cause and coordinate the joint action. However, this condition has typically simply been taken for granted rather than argued for. The condition is not necessary for ensuring that participants are jointly responsible for the action in which each participates, nor for ensuring that each treats the others as partners rather than as social tools. It (...) is thus something of a mystery why the condition is so widely accepted. By rejecting three arguments that could potentially support it, I argue that reductionists should get rid of the condition. I show that two of the arguments fail. While the third argument is intuitively compelling, it builds on key premises that are unavailable to the reductionist. (shrink)