Wireless spectrum is a scare resource, but in practice much of it is under-used by current owners. To enable better use of this spectrum, we propose an auction approach to dynamically allocate the spectrum in a secondary market. Unlike previous auction approaches, we seek to take advantage of the ability to share spectrum among some bidders while respecting the needs of others for exclusive use. Thus, unlike unlicensed spectrum (e.g. Wi-Fi), which can be shared by any device, and exclusive-use licensed spectrum, where sharing is precluded, we enable efficient alloxcation by supporting sharing along side quality-of-service protections. We present SATYA (Sanskrit for “truth”), a strategy proof and scalable spectrum auction algorithm whose primary contribution is in the allocation of a right to contend for spectrum to both sharers and exclusive-use bidders. Achieving strategy proofness in our setting requires appropriate handling of the externalities created by sharing. We demonstrate SATYA’s ability to handle heterogeneous agent types involving different transmit powers and spectrum needs through extensive simulations.