This paper proposes a model for the short-term memory (STM) of unique lists of known items, as, for instance, a phone number. We show that the ability to accurately store such lists in STM depends strongly on interaction with the preexisting long-term memory (LTM) for individual items (e.g., digits). We have examined this interaction in computer simulations of a network based on physiologically realistic membrane conductances, synaptic plasticity processes, and brain oscillations. In the model, seven STMs can be kept active, each in a different gamma-frequency subcycle of a theta-frequency oscillation. Each STM is maintained and timed by an activity-dependent ramping process. LTM is stored by the strength of synapses in recurrent collaterals. The presence of preexisting LTM for an item greatly enhances the ability of the network to store an item in STM. Without LTM, the precise timing required to keep cells firing within a given gamma subcycle cannot be maintained and STM is gradually degraded. With LTM, timing errors can be corrected and the accuracy and order of items is maintained. This attractor property of STM storage is remarkable because it occurs even though there is no LTM that identifies which items are on the list or their order. Multiple known items can be stored in STM, even though their representation is overlapping. However, multiple, identical memories cannot be stored in STM, consistent with the psychophysical demonstration of repetition blindness. Our results indicate that meaningful computation (memory completion) can occur in the millisecond range during an individual gamma cycle.