Given the rapid increase in the number of phasor measurement units (PMU) installed in substations in recent years, it is not unrealistic to assume that most transmission systems will be fully observable by only PMU measurements in the not so distant future. Such a scenario will enable faster and numerically easier state estimation solution which will be non-iterative due to the linearity of the PMU measurement equations. However, as will be shown in this paper, the benefits do not end there and a closer look at these equations reveals further possibilities of simplification and therefore improved performance of state estimators that use only PMU measurements. Specifically, the paper formulates an alternative decoupled solution, which reduces the size of the state estimation problem, increases computational performance yet maintains high solution accuracy. Both state estimation as well as bad data processing can be efficiently carried out within the developed decoupled formulation.