The Psychological Refractory Period (PRP) paradigm is a dual-task procedure that can be used to examine the resource demands of specific cognitive processes. Inferences about the underlying processes are typically based on performance in the second of two speeded tasks. If the effect of a factor manipulated in Task 2 decreases as the stimulus onset asynchrony (SOA) between tasks decreases (underadditivity), the normative inference is that the effect of this factor occurs prior to a limited-capacity central processing mechanism. In contrast, if the effect of a factor is additive with SOA then the inference is that this indexes a process that either uses a limited-capacity central processing mechanism or occurs after some process that uses this mechanism. A heretofore unidentified exception to this logic arises when Task 2 involves two separate processes that operate in parallel, but compete. Interference with one process in Task 2 because of work on Task 1 will eliminate or reduce competition within Task 2 and is hence manifest as an underadditive interaction with decreasing SOA. This is illustrated here by reference to a PRP experiment in which the ubiquitous effect of spelling-to-sound regularity on reading aloud time is eliminated at a short SOA and by consideration of three converging lines of investigation in the PRP paradigm when Task 2 involves reading aloud.