White matter hyperintensities (WMH) or white matter lesions exhibit high variability in their characteristics both at population- and subject-level, making their detection a challenging task. Population-level factors such as age, vascular risk factors and neurodegenerative diseases affect lesion load and spatial distribution. At the individual level, WMH vary in contrast, amount and distribution in different white matter regions. In this work, we aimed to improve BIANCA, the FSL tool for WMH segmentation, in order to better deal with these sources of variability. We worked on two stages of BIANCA by improving the lesion probability map estimation (classification stage) and making the lesion probability map thresholding stage automated and adaptive to local lesion probabilities. Firstly, in order to take into account the effect of population-level factors, we included population-level lesion probabilities, modelled with respect to a parametric factor (e.g. age), in the classification stage. Secondly, we tested BIANCA performance when using four alternative classifiers commonly used in the literature with respect to K-nearest neighbour algorithm (currently used for lesion probability map estimation in BIANCA). Finally, we propose LOCally Adaptive Threshold Estimation (LOCATE), a supervised method for determining optimal local thresholds to apply to the estimated lesion probability map, as an alternative option to global thresholding (i.e. applying the same threshold to the entire lesion probability map). For these experiments we used data from a neurodegenerative cohort, a vascular cohort and the cohorts available publicly as a part of a segmentation challenge. We observed that including population-level parametric lesion probabilities with respect to age and using alternative machine learning techniques provided negligible improvement. However, LOCATE provided a substantial improvement in the lesion segmentation performance, when compared to the global thresholding. It allowed to detect more deep lesions and provided better segmentation of periventricular lesion boundaries, despite the differences in the lesion spatial distribution and load across datasets. We further validated LOCATE on a cohort of CADASIL (Cerebral autosomal dominant arteriopathy with subcortical infarcts and leukoencephalopathy) patients, a genetic form of cerebral small vessel disease, and healthy controls, showing that LOCATE adapts well to wide variations in lesion load and spatial distribution.