In this work an alternative method, named SLICING, for two-dimensional and noniterative T(2) decomposition of low-field pulsed NMR data (LF-NMR) is proposed and examined. The method is based on the Direct Exponential Curve Resolution Algorithm (DECRA) proposed by W. Windig and A. Antalek (1997, Chemom. Intell. Lab. Syst.37, 241-254) and takes advantage of the fact that exponential decay functions, when translated in time, retain their characteristic relaxation times while only their relative amounts or concentrations change. By such simple translations (slicing) it is possible to create a new "pseudo" direction in the relaxation data and thus facilitate application of trilinear (multiway) data-analytical methods. For the application on LF-NMR relaxation data, the method has two basic requirements in practice: (1) two or more samples must be analyzed simultaneously and (2) all samples must contain the same qualities (i.e., identical sets of distinct T(2) values). In return, if these requirements are fulfilled, the SLICING (trilinear decomposition) method provides very fast and unique curve-resolution of multiexponential LF-NMR relaxation curves and, as a spin-off, calibrations to reference data referring to individual proton components require only scaling of the resulting unique concentrations. In this work the performance of the SLICING method (including multiple slicing schemes) is compared to a traditional two-dimensional curve fitting algorithm named MATRIXFIT through application to simulated data in a large-scale exhaustive experimental design and the results validated by application to two small real data sets. Finally a new algorithm, Principal Phase Correction (PPC) based on principal component analysis, is proposed for phase rotation of CPMG quadrature data, an important prerequisite to optimal SLICING analysis.