Even though the logratio methodology provides a range of both generic, mostly exploratory, and purpose-built coordinate representations of compositional data, simple pairwise logratios are preferred by many for multivariate analysis in the geochemical practice, principally because of their simpler interpretation. However, the logratio coordinate systems that incorporate them are predominantly oblique, resulting in both conceptual and practical problems. We propose a new approach, called backwards pivot coordinates, where each pairwise logratio is linked to one orthogonal coordinate system, and these systems are then used together to produce a concise output. In this work, principal component analysis and regression with compositional explanatory variables are used as primary methods to demonstrate the methodological and interpretative advantages of the proposal. In the applied part of this study, sediment compositions from the Jizera River, Czech Republic, were analysed using these techniques through backwards pivot coordinates. This allowed us to discuss grain size control of the element composition of sediments and clearly distinguish anthropogenically contaminated and uncontaminated strata in sediment depth profiles.