It is well-known that multiuser detection techniques such as successive interference cancellation (SIC) can obtain significant performance improvement over traditional matched filter receivers in code division multiple access (CDMA) systems. Due to its simplicity and usefulness, the SIC structure has received significant attention for several years. In this letter, we make three contributions to the understanding of this receiver structure. First, we derive a closed form expression for received power profile of linear SIC with arbitrary spreading gain and SINR requirements. Second, using this expression we examine the performance of SIC under various ordering criteria based on spreading gain, path loss, and SINR/BER requirement. Third, we show that using a very simple and well-known sorting algorithm, we can obtain a cancellation order and set of power control levels which are very near the optimum in terms of minimizing total transmit power.