Peak fitting is an essential part of X-ray photoelectron spectroscopy (XPS) narrow scan analysis, and the Literature contains both good and bad examples of peak fitting. A common cause of poor peak fitting is the inclusion of too many fit parameters, often without a sound chemical and/or physical basis for them, and/or the failure to reasonably constrain them. Under these conditions, fit parameters are often correlated, and therefore lacking in statistical meaning. Here we introduce the uniqueness plot as a simple graphical tool for identifying bad peak fits in XPS, i.e., fit parameter correlation. These plots are widely used in spectroscopic ellipsometry. We illustrate uniqueness plots with two data sets: a Cls narrow scan from ozone-treated carbon nanotube forests and an Si 2p narrow scan from an air-oxidized silicon wafer. For each fit, we consider different numbers of parameters and constraints on them. As expected, the uniqueness plots are parabolic when fewer fit parameters and/or more constraints are applied. However, they fan out and eventually become horizontal lines as more unconstrained parameters are included in the fits. Uniqueness plots are generated by plotting the chi squared (chi(2)) value for a fit vs. a systematically varied value of a parameter in the fit. The Abbe criterion is also considered as a figure of merit for uniqueness plots in the Supporting Information. We recommend that uniqueness plots be used by XPS practitioners for identifying inappropriate peak fits. (C) 2016 Elsevier B.V. All rights reserved.