Aerial Manipulators with Elastic Suspension (AMES) may be seen as a hybrid robot mixing properties of classical Aerial Manipulators (AMs) and Cable-Driven Parallel Robots (CDPRs). The optimal design and control of an AMES using unidirectional thrusters are considered in this paper. To maximize the workspace, an optimization algorithm is proposed. The position and orientation of the thrusters are optimized by adapting methods borrowed from both the AM and CDPR communities. The resulting design is used to build a prototype. Preliminary experimentations are carried out to validate the theoretical workspace and assess the trajectory tracking performance of this AMES. Experiments highlight the significant improvements with respect to a previous suboptimal prototype.