The design of distribution use-of-system tariffs has been traditionally driven by long-term cost recovery considerations. However, the emerging large-scale integration of distributed energy resources motivates the value of tariffs that are more adaptive to short-term conditions, in order to exploit the inherent flexibility of distributed energy resources and consequently increase the economic efficiency of distribution network operation. This paper addresses the problem of short-term distribution use-of-system tariffs design through a bilevel optimization model, capturing the interaction between a distribution system operator at the upper level and prosumers with distributed energy resources at the lower level. In contrast to previous relevant literature, this model considers a detailed representation of the power flow constraints, different levels of temporal and spatial granularity in the designed tariffs, as well as discrete tariff levels for preserving intelligibility. Furthermore, instead of relying on exogenous typical days, the developed model employs a clustering approach to design tariffs that adapt to the forecasted conditions of the upcoming day. The examined case studies demonstrate the impacts of different levels of tariff granularity on economic efficiency, and test the performance of the proposed clustering approach through out-of-sample simulations involving different scenarios regarding the selected number of clusters.