Many pseudo function techniques for representing waterflood performance in stratified reservoirs make direct, or indirect, assumptions regarding the constancy of saturation velocities. For simple models, inspection of analytical model results shows that curved saturation velocity characteristics can be expected to occur at non-unit mobility ratio flow conditions. Failure to incorporate the effect of changing saturation velocity is shown to be the underlying reason for the poor agreement displayed by many pseudo function techniques. Curved characteristics are not compatible with any of the previously accepted models for pseudo functions. This incompatibility can be resolved through the introduction of length dependency of the upscaled pseudo functions. By considering displacements in an idealized system, this work demonstrates deficiencies with previous pseudo function approaches and demonstrates that, with an allowance for length dependency, an improved upscaled representation of the displacement can result.