In this paper, we propose to reduce the effect of rate-independent MAC overheads in random access protocols by partitioning the transmission channel spectrum into a narrow channel and a wide channel. The narrow channel is used for transmitting the short packets (approximately 100 bytes long) and the wide channel is used for transmitting the longer packets. We intend to use multiple radios, one each for the different channel partitions. Narrow width channels have a reduced capacity, which lowers the maximum transmission rate achievable on these channels. As a result, the channel wastage due to the rate-independent MAC overheads can be reduced. We propose a protocol called WiSP (channel Width Selection based on Packet size) to estimate the appropriate channel widths depending on the relative traffic load involving short and long packets in the network. We evaluate our protocol using extensive simulations and demonstrate its effectiveness in achieving higher throughputs. We propose our algorithm to complement the frame aggregation (an existing approach that aggregates multiple packets to be sent in a single transmit opportunity) technique. We show that there are scenarios during which the frame aggregation can perform poorly, and show that our proposed algorithm can provide a good performance even in those situations when used along with frame aggregation.