This paper proposes a new scheme coupling power control with a minimum outage probability multiuser detector. The resultant iterative algorithm is conceptually simple and finds the minimum sum transmission power of all users with a set of outage probability constraints. Bounds on the outage probability expression are found that extend a previous result that did not include receiver noise. These bounds are used to create a suboptimal scheme coupling power control and a MMSE multiuser detector. This new problem becomes a variant of an existing problem where outage probability constraints are first mapped to average SIR threshold constraints. Simulation results are presented showing the closeness of the two schemes and speed of convergence.