A methodology using the standardised precipitation index is proposed to develop critical drought intensity-duration-frequency (IDF) curves. We define dry periods within which we recognise droughts of different durations. The most severe drought for each drought duration in each year is called the critical drought. The total probability theorem-coupled frequency analysis is used to determine the best-fit probability distribution function of drought severity, which is then converted to intensity. The generalised extreme value probability distribution function is found to best fit the critical drought severity. The methodology is implemented using monthly precipitation data for a meteorological station in Turkey. The critical drought intensity decreases linearly with increasing drought duration, whereas the return period increases exponentially when the drought becomes more severe. The site-specific IDF curves furnished with an empirical relationship between the intensity and return period allow one to characterise the drought not by an index-based intensity but by its return period. This kind of presentation is physically easier to understand, in particular for stakeholders and decision makers in practice.