This paper focuses on the problem of code acquisition in multiuser CDMA systems in a near-far scenario. A new time offset estimator which iteratively cancels interference from correctly acquired users is proposed. Interference cancellation is accomplished by projecting the received signal into the null space of already acquired users. The proposed technique performs well under low SNR conditions in the presence of high multiple access interference. Analytical expressions for the missed detection probability of the proposed estimator are derived and these agree with the results of Monte-Carlo simulations.