A typical wireless sensor network consists of many small sensors that collect instrument data around their locations and forward it to a central location for data processing. These networks can be deployed to monitor livestock and agricultural assets, products in a store, patients in a hospital, and so on. In many cases sensors have to be densely deployed, and collisions or overhead due to collision avoidance will considerably degrade the system performance below an application's required levels. With the decreasing cost of radio devices the obvious solution to this problem is the use of multiple receivers on different radio channels. However, we show that if receivers can be placed in different locations then increasing the number of receivers on a single channel will increase the rate of the capture effect and decrease collision losses, while also increasing the fairness of the transmitters' radio links. Not only can this single channel approach be more effective than using multiple channels, it is also required for some techniques, such as localization, where each receiver must be able to detect a transmission from any transmitter. We also show that the optimal choice between these two solutions is influenced by the radio attenuation rate and the number of receivers in the system.