The first step in reasoning using an approach such as ASPIC+ requires all arguments to be generated, and doing so is computationally intensive when encountering large or frequently updated defeasible theories. In this paper, we introduce the informative partial argumentation framework that enables us to control and customise the argument construction process, potentially improving computational efficiency. In our framework, arguments are constructed in a lazy manner; and through the modularisation of our framework, it is possible to restrict the amount of computation to only the necessary information.