Recently, a new technique for unique non-iterative multi-exponential fitting of time domain NMR data was proposed. The method was termed SLICING, because an intrinsic part of the method consisted of taking different parts (slices) of the original matrix data and rearranging the slices into a three-way box of data. Subsequently, a directly calculated model of this box provided T(2)-estimates and corresponding amplitudes. The most critical part of this method is the choice of how to slice the original data. In this paper, a new general scheme for this slicing is proposed which (1) is shown to provide more accurate T(2)-estimates and (2) leads to a significant speed improvement compared to earlier approaches. The method is called PowerSlicing, because it takes slices of lag 2(x) (x=0,1,..,N) where 2(N) < or =J/2 and J is the number of bins on the time axis. This approach ensures a reasonably high amount of direct constraints and an appropriate representation of both short and long time decays in the decomposition.