Recently, we have extended the damped-technique in the modified BFGS method of Powell for constrained optimization to the Broyden family of quasi-Newton methods for unconstrained optimization. Appropriate conditions on the damped parameter will be suggested to maintain the convergence property of a restricted Broyden family of methods, to improve the performance of convergent methods and to enforce convergence of 'undamped' divergent methods. These properties will be illustrated on simple and general optimization problems. It will be shown that the proposed damped choices improve the performance of some quasi-Newton methods substantially (and significantly) in several cases.