Quantum Optimal Control (QOC) describes a family of techniques that improve quantum operations by systematically shaping the dynamic control fields applied to the system [1]. It has become an important tool to improve the performance of quantum technological applications [2]. Most QOC algorithms rely on parameterising the pulse shape with a set of basis functions. The piecewise-constant basis, for example, is likely the most commonly used basis. Here, the pulse is split up into time steps and each step’s amplitude is mapped to a parameter, which is then optimised iteratively. Other bases, such as the Fourier basis composed of frequency elements, have found their application too [3]. The basis choice typically falls on what is most standard for the implemented QOC algorithm. But does the basis influence the quality of the optimisation? We test different bases on QOC problems of varying complexity to understand their effect [4]. To emulate a closed-loop (experimental) setting, where measurements are expensive, we use a gradient-free dressed Chopped RAndom Basis (dCRAB) [3] algorithm. We consider three bases: First, the Fourier basis represents the standard choice. Second, the sigmoid basis is a limited-bandwidth CRAB-equivalent of the piecewise-constant basis [5]. Lastly, the sinc basis provides a constant bandwidth approach. Our findings show that the convergence rate of the optimisation is highly dependent on the employed basis and that their ranking differs for each problem. We conclude that a problem-dependent basis choice is an influential factor for QOC efficiency and provide advice for its approach. Hopefully, our results will lead to more efficient applications of QOC in the future.