We investigate the use of adaptive minimum bit error rate (MBER) gradient-Newton algorithms in the design of linear multiuser receivers (MUD) for DS-CDMA systems. The proposed algorithms approximate the bit error rate (BER) from training data using linear multiuser detection structures. We carry out a comparative analysis of linear MUDs employing minimum mean squared error (MMSE), previously reported MBER and the proposed MBER algorithms. Computer simulation experiments show that the MBER gradient-Newton approaches outperform other analysed algorithms and can operate with shorter training sequences.