Since code division multiple access systems in multipath environments suffer from multiple access interference (MAI), multiuser detection schemes should be used in the receivers. Parallel interference cancellation (PIC) is a promising method to combat MAI due to its relatively low computational complexity and good performance. It is shown in this paper that the complexity of PIC is still high for realistic scenarios in terms of the symbol rate, the number of users, spreading gain, and multipath components. However, two novel methods are introduced to reduce significantly the complexity without sacrificing performance. The first approach, called reduced PIC, takes advantage of the composition of the interference to concentrate interference cancellation only on significant terms. The second approach, called differential PIC, exploits the multistage character of PIC to avoid unnecessary double calculations of certain terms in consecutive stages. It is shown that a combination of both approaches leads to a performance very close to the single-user bound whereas the complexity can be kept on the order of the conventional RAKE receiver.