In the state-space approach to H optimal control, feasibility of some closed-loop attenuation g is characterized in terms of a pair of game Riccati equations depending on g. This paper is concerned with the properties of these equations as g varies. The most general problem is considered (D11 0) and a thorough analysis of the variations of the Riccati solutions provides insight into the behavior near the optimum and into the dependence on g of the suboptimality conditions. In addition, concavity is established for a criterion which synthesizes the three conditions X 0, Y 0, and p(XY) < g 2. As a result, a numerically reliable Newton scheme can be devised to compute the optimal g. Most presented results are extensions of earlier contributions. The main concern here is to provide a complete and synthetic overview as well as results and formulas tailored to the development of numerically-sound algorithms.