All spatio-temporal grain-size patterns in sediments can be characterized by a mathematical representation of (un)mixing. This implies that an inverse model of (un)mixing would be ideally suited to obtain genetically meaningful interpretations of observed grain-size distributions (GSDs). GSDs are therefore often decomposed into theoretical end members by parametric curve-fitting procedures. Many researchers have been tempted to use goodness-of-fit measures as a means of justifying such decompositions in the absence of generic process-based models of end-member GSDs. A critical examination of parametric curve fitting through a series of numerical experiments shows that the goodness-of-fit of an approximation may be a poor guide to its genetic significance. The genetic interpretation of GSDs is a poorly constrained problem that cannot be solved without taking into account the geological context of GSDs, which may be captured by the covariance structure of grain-size classes across a series of GSDs sampled in a contiguous area. Curve-fitting methods cannot exploit this geological context, which explains why the geological relevance of curve-fitting results obtained in black-box mode is questionable. The desired genetic interpretation of GSDs can be obtained by applying the end-member-modelling algorithm EMMA to a series of GSDs simultaneously. Many end-member GSDs estimated by EMMA do not conform to one of the popular theoretical GSD models. Consequently, parametric curve fitting with theoretical distributions is more likely to obscure than to reveal the existence of genetically significant grain-size populations in sediments, especially if such populations are present in small proportions. © 2007 Elsevier B.V. All rights reserved.