Tightly coupled arrays are a class of antenna arrays that are very wideband and have applications in communication and sensor systems. In both applications, low side-lobe levels are of interest. However, as tightly coupled arrays have high inter-element coupling, care must be taken when finding a suitable set of excitation coefficients. To demonstrate this, we design a tightly coupled array. Second, we extend a previously published convex optimization algorithm to account for strong inter-element coupling. This optimization algorithm solely finds excitations implementable in a simplified hardware model. The results are compared with conventional taperings, and show that our algorithm can achieve an excitation with lower reflected power compared to the conventional taperings, while maintaining similar gain and side-lobe levels.