Optimal H(infinity)-fixed-point and fixed-lag discrete-time smoothing estimators are developed by applying a game theory approach. A deterministic discrete-time game is defined where the estimator plays against nature. Nature determines the system initial condition, the driving input, and the measurement noise, whereas the estimator tries to find an estimate that brings a prescribed cost function that is based on the error of the estimation at a fixed time instant, to a saddle-point equilibrium. The latter estimate yields the H(infinity)-optimal fixed-point smoothing. Differently from the usual case in H(infinity)-optimal estimation and control, the critical value of the scalar design parameter of the smoothing game is obtained in closed form, explicitly in the terms of the corresponding H-2 solution. Unlike the H-2 case, the recursive application of the H(infinity) fixed-point smoothing algorithm does not lead to fixed-lag smoothing in the H(infinity)-norm sense. The H(infinity) fixed-lag smoothing filter is derived by augmenting the state vector of the system with additional delayed states.