Contoured bearing surfaces forming continuous surface pockets in slider bearings increase the load carrying capacity considerably. Article investigates the effect of two dimensionally contoured surfaces of a few sample shapes on the performance characteristics of hydrodynamic slider bearings. Exponential and trigonometric film shapes are considered. Computer-aided numerical finite difference solution of the two-dimensional Reynolds equation is used via a self mesh generating computer program, which also generates optimum design data including dimensionless load-, flow-, temperature rise-, power loss-, stiffness-, damping, and friction coefficients. Optimum bearings are defined as the maximum load capacity bearings. Optimum design charts are given, where dimensional ratios and powers of exponents are optimized. Lubricant is incompressible with temperature dependent viscosity. The effect of temperature is considered by maintaining energy balance via iterative thermal loop. In comparison to optimum one-dimensional tapered film bearings gains of over 200% in the load capacities of contoured narrow bearings are observed.