A highly useful tool, called the race inequality, was introduced by Miller (1982) and has since been widely implemented. When the inequality is violated, ordinary parallel race models are falsified. In addition, within a general theory of processing capacity (Townsend & Nozawa, 1988, 1992), it is shown that capacity must be "super" if the inequality is violated. However, we here exhibit the seemingly paradoxical result that serial models with an exhaustive processing rule can violate the inequality. Exhaustive serial processing is typically viewed as the antithesis of unlimited capacity parallel processing, not to mention super capacity processing. Our theoretical finding is discussed with respect to a deeper and more relative, notion of capacity and suggestions are made with regard to ruling out such "artifacts" through the employment of rigorously derived convergent experimental conditions.