This paper deals with the optimisation of a sequence and its associated mismatched filter. This question has already been addressed in the literature, by alternatively solving two minimisation problem, one per sequence, meaning that the optimisation is never performed on both sequences at the same time. So, this article introduces some methods in order to optimise jointly (i.e. simultaneously) a sequence and its filter. First, a gradient descent is basically applied on both sequences. Second, another algorithm studies an objective function that includes the optimal mismatched filter that minimises the Integrated Sidelobe Level (or the Peak-to-Sidelobe Level Ratio). Simulations show promising results in terms of sidelobes: as expected, a joint optimisation seems to perform better than a separate one. As both methods behave differently, their choice will depend on the applications.