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We consider a symbol-synchronous code-division multiple-access (CDMA) system that is equipped with a multiuser decision-feedback receiver and for which power control is available. The users are each assigned a quality-of-service (QoS) threshold to be guaranteed by the system, and to cover scenarios for which there are multiple classes of users, these are not required to be equal to each other. For an ideal decision-feedback receiver, it is known that with enough power the system can always meet the users' QoS thresholds, so we instead minimize the sum of the users' received powers over system designs (i.e., signature sequences, power-control policy, and decision-feedback receiver) which guarantee the QoS requirements. It is found that the optimal design produces two classes of users, those whose sequences and powers satisfy with equality the generalized Welch bound inequality and those oversized users that are mutually orthogonal to each other and the rest of the users. In terms of power and bandwidth savings, the optimal sequences for the decision-feedback receiver are found to compare very favorably to optimal designs for linear receivers and to random sequences for the decision-feedback receiver.