Bubble technology offers several operations that have no equivalents in technologies based on magnetic recording. Examples of such operations are transfer, reversal of the direction of propagation, and opening and closing of gaps in the data stream. This paper shows how such operations can be used to dynamically reallocate data in the bubble memory, causing it to become an integrated memory hierarchy. A model is presented which relates the bubble memory with dynamic reallocation to stack processing, a technique used in the evaluation of memory hierarchies. With the aid of this model it becomes possible to calculate the performance of the bubble memory using published data derived from the traces of selected typical programs. Design parameters are proposed for a 2 Mbit bubble memory with 128 detectors which in the execution of such programs requires an average of only 8.8 shifts for access and an average of 12 shifts per memory cycle. If bubbles are propagated at a rate of 1 MHz, the average access and cycle times for this memory become 8.8 μs and 12μs, respectively. Such performance, in combination with the low cost per bit offered by bubble technology, is expected to have a major impact.