A longstanding goal of SSD virtualization has been to provide performance isolation between multiple tenants sharing the device. Virtualizing SSDs, however, has traditionally been a challenge because of the fundamental tussle between resource isolation and the lifetime of the device - existing SSDs aim to uniformly age all the regions of flash and this hurts isolation. We propose utilizing flash parallelism to improve isolation between virtual SSDs by running them on dedicated channels and dies. Furthermore, we offer a complete solution by also managing the wear. We propose allowing the wear of different channels and dies to diverge at fine time granularities in favor of isolation and adjusting that imbalance at a coarse time granularity in a principled manner. Our experiments show that the new SSD wears uniformly while the 99th percentile latencies of storage operations in a variety of multi-tenant settings are reduced by up to 3.1x compared to software isolated virtual SSDs.