This paper presents a new modelling of positive-discharge development, based on new simplifying assumptions. It presents these assumptions, which are deduced from the existing theoretical models and concern mainly the coupling between the leader corona and the corona region. This model has been validated through the comparison of simulations with experimental results in the reference configuration of a rod - plane gap subjected to various positive impulse voltages. It has also been used to simulate the discharge behaviour with perturbations of the applied potential form.