This paper revisits the no-trade theorem by explicitly modeling a margin that is usually kept implicit: agents must be able to process the informational content of what they observe without cost. The paper formalizes the argument in a minimal bilateral risky-asset environment with a two-stage structure. The buyer's problem reduces to a one-dimensional maximization of an indirect certainty-equivalent objective; the interior optimum equates the marginal processing cost with the marginal value of precision. The key mechanism is the role of equilibrium objects (i.e., prices) in aligning beliefs under rational expectations. We show that swamping's cognitive prerequisite --- costless conditioning on the public object --- fails whenever the processing intensity is finite, and that this failure is endogenous: agents optimally choose the degree of failure by equating the marginal value and marginal cost of precision; this failure has equilibrium consequences.