We derive upper and lower bounds on the absorption of ultraintense laser light by solids as a function of fundamental laser and plasma parameters. These limits emerge naturally from constrained optimization techniques applied to a generalization of t
he laser-solid interaction as a strongly-driven, relativistic, two degree of freedom Maxwell-Vlasov system. We demonstrate that the extrema and the phase-space-averaged absorption must always increase with intensity, and increase most rapidly when $10^{18} < I_L lambda_L^2 < 10^{20}$ W $mu$m$^2/$cm$^{2}$. Our results indicate that the fundamental empirical trend towards increasing fractional absorption with irradiance therefore reflects the underlying phase space constraints.
