The design and analysis of multistage detectors with universal weights for asynchronous CDMA systems is presented. The use of a front-end that enables joint detection and provides sufficient statistics is proposed. With such a front end the proposed multistage detector has the same complexity order per bit as the matched filter. The proposed approach can also take into account other suboptimum statistics and the non-ideality of the chip pulse waveforms. In such a way, the universal weights can be designed and the performance can be computed for very realistic scenarios.