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 choices for the damped parameter will be suggested to maintain the convergence property of a restricted Broyden family of methods and to enforce convergence of the divergent methods. These properties will be illustrated on simple and general problems. It will be shown that the proposed damped choices improve the performance of most quasi-Newton methods substantially (or significantly) in several cases. We will also illustrate the useful features of the self-scaling technique for quasi-Newton methods and a possible combination of the above two techniques.