The issue of non-cooperative transceiver optimization in the uplink of a multiuser wireless data network with widely linear detection at the receiver is considered in this paper. While previous work in this area has focused on a simple real signal model, in this paper a baseband complex representation of the data is used, so as to properly take into account the I and Q components of the received signal. For the case in which the received signal is improper, a widely-linear reception structure, processing separately the data and their complex conjugates, is considered. The convergence of the well-known minimum mean square error (MMSE) iteration for spreading code adaptation is studied for the case in which widely-linear detection is used at the receiver. Interestingly, it is also found that spreading code optimization coupled with widely-linear filtering permits supporting, with no multiuser interference, a number of users that is twice the processing gain. Numerical results corroborate the validity of the theoretical analysis, and show that exploiting the improper nature of the data in non-cooperative resource allocation brings remarkable performance improvements in multiuser wireless systems.