Recently, a novel class of low-pressure nanofiltration (NF) hollow fiber membranes, particularly suited for water softening and desalination pretreatment have been fabricated in-house using layer-by-layer (LbL) deposition with chemical crosslinking. These membranes can operate at exceedingly low pressures (2 bar), while maintaining relatively high rejections of multivalent ions. In spite of their great potential, our understanding as to what makes them superior has been limited, demanding further investigation before any large-scale implementation can be realized. In this study, the Donnan-Steric Pore Model with dielectric exclusion (DSPM-DE) is applied for the first time to these membranes to describe the membrane separation performance, and to explain the observed rejection trends, including negative rejection, and their underlying multi-ionic interactions. Experiments were conducted on a spectrum of feed chemistries, ranging from uncharged solutes to single salts, salt mixtures, and artificial seawater to characterize the membrane and accurately predict its performance. Modeling results were validated with experiments, and then used to elucidate the working principles that underlie the low-pressure softening process. An approach based on sensitivity analysis shows that the membrane pore dielectric constant, followed by the pore size, are primarily responsible for the selectively high rejections of the NF membranes to multivalent ions. Surprisingly, the softening process is found to be less sensitive to changes in membrane charge density. Our findings demonstrate that the unique ability of these membranes to exclusively separate multivalent ions from the solution, while allowing monovalent ions to permeate, is key to making this low-pressure softening process realizable. (C) 2016 Elsevier B.V. All rights reserved.