Many wireless channels in different technologies are known to have partial overlap. However, due to the interference effects among such partially overlapped channels, their simultaneous use has typically been avoided. In this paper, we present a first attempt to model partial overlap between channels in a systematic manner. Through the model, we illustrate that the use of partially overlapped channels is not always harmful. In fact, a careful use of some partially overlapped channels can often lead to significant improvements in spectrum utilization and application performance. We demonstrate this through analysis as well as through detailed application-level and MAC-level measurements. Additionally, we illustrate the benefits of our developed model by using it to directly enhance the performance of two previously proposed channel assignment algorithms --- one in the context of wireless LANs and the other in the context of multi-hop wireless mesh networks. Through detailed simulations, we show that use of partially overlapped channels in both these cases can improve end-to-end application throughput by factors between 1.6 and 2.7 in different scenarios, depending on wireless node density. We conclude by observing that the notion of partial overlap can be the right model of flexibility to design efficient channel access mechanisms in the emerging software radio platforms.