The relative intensities of H I and He II recombination lines are calculated, including full collisional effects, for a considerably larger range of temperature, density and principal quantum numbers than before. Case B of Baker & Menzel is assumed, and tables of line opacities are also presented to enable the assumption of negligible optical depth in all but the Lyman series to be checked. Collisional excitation of the n = 3 levels from both n = 1 and n = 2 states is considered, and is found to invalidate Case B theory in some conditions which depend on electron density and the Lyman-α escape probability. The regimes of temperature and particle density for which Case B is valid are discussed. Newly calculated collision strengths for the n = 1, 2 and 3 states of He⁺ are tabulated.