Minimum convex polygons (convex hulls) are an internationally accepted, standard method for estimating species' ranges, particularly in circumstances in which presence-only data are the only kind of spatially explicit data available. One of their main strengths is their simplicity. They are used to make area statements and to assess trends in occupied habitat, and are an important part of the assessment of the conservation status of species. We show by simulation that these estimates are biased. The bias increases with sample size, and is affected by the underlying shape of the species habitat, the magnitude of errors in locations, and the spatial and temporal distribution of sampling effort. The errors affect both area statements and estimates of trends. Some of these errors may be reduced through the application of α-hulls, which are generalizations of convex hulls, but they cannot be eliminated entirely. α-hulls provide an explicit means for excluding discontinuities within a species range. Strengths and weaknesses of alternatives including kernel estimators were examined. Convex hulls exhibit larger bias than α-hulls when used to quantify habitat extent and to detect changes in range, and when subject to differences in the spatial and temporal distribution of sampling effort and spatial accuracy. α-hulls should be preferred for estimating the extent of and trends in species' ranges.