Systems containing both real parametric uncertainty and weighted-ball-in-H?? uncertainty are addressed. The concept of robustness given perfect parameter information is reviewed. Robust parameter estimation laws designed for maximal convergence in the presence of non-parametric ball-in-H?? uncertainty are reviewed. It is shown that if the control laws would produce a robust design given perfect parameter information, and if the robust estimation laws are used in lieu of knowledge of the parameters robust bounded-L2-input bounded-L2-output (L2-BIBO) stability automatically results. Shortcomings of BIBO stability are discussed.