Previous studies have shown that the effect of concurrent nontemporal processing on time estimation may vary depending on the level of difficulty of the nontemporal task. This is commonly interpreted within the context of so-called distraction/interruption models of temporal processing, which propose that as concurrent task difficulty or complexity is increased, temporal processing receives less attention. We hypothesize that the effect of nontemporal processing does not depend on the level of difficulty as such, but rather on the extent to which the concurrent nontemporal task specifically involves processing in short-term memory. Four experiments were run in which the short-term memory requirements of concurrent tasks were systematically varied, although all of the tasks were of comparable levels of difficulty. In the first experiment, the effect of memory search on simultaneous temporal productions was proportional to the number of items to search. As with reaction time, produced intervals were shown to increase linearly with the number of items in the memorized set. In Experiment 2, a visual search involving some load on short-term memory interfered in the same way with time production, although to a lesser extent. The last two experiments showed that performing attention-demanding visual search tasks that did not involve short-term memory did not lengthen simultaneously produced time intervals. This suggests that interference of nontemporal processing on time processing may not be a matter of nonspecific general purpose attentional resources, but rather of concurrent short-term-memory processing demands.