Data mining is supposed to be an iterative and exploratory process, not a one-shot exercise. In this context, we are working on a project whose overall objective is to develop a practical computing environment for human-centred, exploratory mining of frequent sets. One critical component of such an environment is the support for dynamic mining of constrained frequent sets. Constraints enable the user to impose certain focus on the mining process, while dynamic means, in the middle of the computation, the user will be able to: (i) tighten, relax, or change the constraints, and/or (ii) change the minimum support threshold, thus having a decisive influence on subsequent computation. In a real-life situation, the available buffer space may be limited, thus adding another complication to the problem. In this paper, we develop an algorithm called DCF, for Dynamic Constrained Frequent set computation. This algorithm is enhanced with a few optimizations, exploiting a lightweight structure called a segment support map. It enables DCF to (i) obtain sharper bounds on the support of sets of items, and to (ii) better exploit properties of constraints. DCF relies on the concept of a delta member generating function, which generates precisely the sets of items that satisfy the new but not the old constraints. Our experimental results show the effectiveness of these enhancements.