There is often strong interference if a second target stimulus (T2) is presented before processing of a prior target stimulus (T1) is complete. In the "Psychological Refractory Period" (PRP) paradigm, responses are speeded and interference manifests as increased response time for T2. In the "Attentional Blink" (AB) paradigm, stimuli are masked and responses unspeeded; interference manifests as reduced T2 accuracy. While different causes have usually been considered for PRP and AB phenomena, recent evidence has supported a unified account based on a single, shared restriction on concurrent processing. Here we show that a full assessment of separate and shared resource limitations requires direct comparison of hybrid PRP/AB trials with corresponding pure PRP and AB cases. Randomizing trial types in such a comparison also brings substantial benefit in addressing possible changes in task preparation or readiness. The data from two such experiments--combining speeded auditory (SA) and unspeeded visual (UV) task events--provide clear evidence for both separate and shared resource limitations. Often interference is strongest for T1 and T2 events of the same type, reflecting predominantly different limitations in SA and UV processing. With modest increases in demand, however, interference between different event types can also be made arbitrarily large, reflecting arbitrarily important shared limitations. For even such simple tasks as these, T1-T2 interference reflects a combination of relatively local and relatively global sources. [This work was supported by the Human Frontier Science Program.]