In this paper, a new tensegrity generation method, based on a combination of a random search, quadratic programming and connection pruning is proposed. The method exploits the structure of the static equilibrium equations of tensegrity structures with static nodes, allowing to form linear equality constraints. By abandoning the requirement of struts being disconnected we arrive at a simple convex program, where the existence of solution represents the existence of the sought structure. We propose a way to generate node positions and to prune the connections in order to shape the resulting tensegrity-like structures in the desired form.