Studies exploring the role of neural oscillations in cognition have revealed sustained increases in alpha-band (∼8–14 Hz) power during the delay period of delayed-recognition short-term memory tasks. These increases have been proposed to reflect the inhibition, for example, of cortical areas representing task-irrelevant information, or of potentially interfering representations from previous trials. Another possibility, however, is that elevated delay-period alpha-band power (DPABP) reflects the selection and maintenance of information, rather than, or in addition to, the inhibition of task-irrelevant information. In the present study, we explored these possibilities using a delayed-recognition paradigm in which the presence and task relevance of shape information was systematically manipulated across trial blocks and electroencephalographic was used to measure alpha-band power. In the first trial block, participants remembered locations marked by identical black circles. The second block featured the same instructions, but locations were marked by unique shapes. The third block featured the same stimulus presentation as the second, but with pretrial instructions indicating, on a trial-by-trial basis, whether memory for shape or location was required, the other dimension being irrelevant. In the final block, participants remembered the unique pairing of shape and location for each stimulus. Results revealed minimal DPABP in each of the location-memory conditions, whether locations were marked with identical circles or with unique task-irrelevant shapes. In contrast, alpha-band power increases were observed in both the shape-memory condition, in which location was task irrelevant, and in the critical final condition, in which both shape and location were task relevant. These results provide support for the proposal that alpha-band oscillations reflect the retention of shape information and/or shape–location associations in short-term memory.