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This paper discusses and optimizes an HMM/GMM based User-Customized Password Speaker Verification (UCP-SV) system. Unlike text-dependent speaker verification, in UCP-SV systems, customers can choose their own passwords with no lexical constraints. The password has to be pronounced a few times during the enrollment step to create a customer dependent model. Although potentially more ``user-friendly'', such systems are less understood and actually exhibit several practical issues, including automatic HMM inference, speaker adaptation, and efficient likelihood normalization. In our case, HMM inference (HMM topology) is performed using hybrid HMM/MLP systems, while the parameters of the inferred model, as well as their adaptation, will use GMMs. However, the evaluation of a UCP-SV baseline system shows that the background model used for likelihood normalization is the main difficulty. Therefore, to circumvent this problem, the main contribution of the paper is to investigate the use of multiple reference models for customer acoustic modeling and multiple background models for likelihood normalization. In this framework, several scoring techniques are investigated, such as Dynamic Model Selection (DMS) and fusion techniques. Results on two different experimental protocols show that an appropriate selection criteria for customer and background models can improve significantly the UCP-SV performance, making the UCP-SV system quite competitive with a text-dependent SV system. Finally, as customers' passwords are short, a comparative experiment using the conventional GMM-UBM text-independent approach is also conducted.