The possibility of constructing non-axisymmetric tension cones is examined with the goal of creating a tension cone that naturally trims to a non-zero angle of attack. The shape derivation for axisymmetric tension cones is used to map a design space from which an initial shape for a non-axisymmetric tension shell can be constructed. A version of the US3D flow solver with fluid-structure interaction (FSI) capabilities is used as a tool for both design and evaluation. Variations 011 the degree of non-symmetry are compared in terms of aerodynamic and structural performance. It is found that simple modifications to the basic tension cone design can result in an inflatable decelerator that trims to an angle of attack of at least 28°, with an L/D of 0.49, while still maintaining a state of pure tension in the tension shell.