This paper explores the use of entropy-based measures in catchment hydrology, and provides an importance-weighted numerical descriptor of the flow-duration curve. Although entropy theory is being applied in a wide spectrum of areas (including environmental and water resources), artefacts arising from the discrete, under-sampled and uncertain nature of hydrological data are rarely acknowledged, and have not been adequately explored. Here, we examine challenges to extracting hydrologically meaningful entropy measures from a flow signal; the effect of binning resolution on calculation of entropy is investigated, along with artefacts caused by (1) emphasis of information theoretic measures towards flow ranges having more data (statistically dominant information), and (2) effects of discharge measurement truncation errors. We introduce an importance-weighted entropy-based measure to counter the tendency of common binning approaches to over-emphasise information contained in the low flows which dominate the record. The measure uses a novel binning method, and overcomes artefacts due to data resolution and under-sampling. Our analysis reveals a fundamental problem with the extraction of information at high flows, due to the lack of statistically significant samples in this range. By separating the flow-duration curve into segments, our approach constrains the computed entropy to better respect distributional properties over the data range. When used as an objective function for model calibration, this approach constrains high flow predictions, as well as the commonly used Nash-Sutcliffe efficiency, but provides much better predictions of low flow behaviour.