Judicial discretion is a central question in both the theory and the practice of law, but it received very little explicit attention from AI&Law yet. What is more, it is often considered as the limitation of what can be formalized in law, which might have serious implications for the future of computational law. In this paper, we introduce a deontic logic extended with nuanced permissions pursuing to grasp the characteristics, normative framework of and reasoning process in the discretionary decision-making of the judge. We illustrate the modeling capacity of the Discretionary Judicial Decision Logic (DJDL) by formalizing examples from an area of law where discretion plays an openly crucial role: family law, more precisely child custody cases.