White matter hyperintensities (WMHs) are well-established markers of cerebral small vessel disease, and are associated with an increased risk of stroke, dementia, and mortality. Although their prevalence increases with age, small and punctate WMHs have been reported with surprisingly high frequency even in young, neurologically asymptomatic adults. However, most automated methods to segment WMH published to date are not optimized for detecting small and sparse WMH. Here we present the SHIVA-WMH tool, a deep-learning (DL)-based automatic WMH segmentation tool that has been trained with manual segmentations of WMH in a wide range of WMH severity. We show that it is able to detect WMH with high efficiency in subjects with only small punctate WMH as well as in subjects with large WMHs (i.e., with confluency) in evaluation datasets from three distinct databases: magnetic resonance imaging-Share consisting of young university students, MICCAI 2017 WMH challenge dataset consisting of older patients from memory clinics, and UK Biobank with community-dwelling middle-aged and older adults. Across these three cohorts with a wide-ranging WMH load, our tool achieved voxel-level and individual lesion cluster-level Dice scores of 0.66 and 0.71, respectively, which were higher than for three reference tools tested: the lesion prediction algorithm implemented in the lesion segmentation toolbox (LPA: Schmidt), PGS tool, a DL-based algorithm and the current winner of the MICCAI 2017 WMH challenge (Park et al.), and HyperMapper tool (Mojiri Forooshani et al.), another DL-based method with high reported performance in subjects with mild WMH burden. Our tool is publicly and openly available to the research community to facilitate investigations of WMH across a wide range of severity in other cohorts, and to contribute to our understanding of the emergence and progression of WMH.