An analytical study of the compressibility effects on the characteristics of two-dimensional slider bearings is made. By the variational method, it is shown that, for a given bearing length, no optimal film shape of the bearing can be found to yield a maximum total load. Analysis of the numerical results carried out for stepped films with a compressible lubricant under isothermal compression or expansion indicates that this anomaly is due to the nonlinear nature of the compressible problem. By considering a modified variational problem, it is further shown that stepped-film bearings with isothermal lubricant still yield the maximum total load for a given mass flow rate passing through the bearings, but the exact shape of the optimal stepped film is found to depend on the value of the maximum pressure.