A cost function for use in an encoding mode decision for encoding a section of a digital picture is determined using a non-default relationship between Lagrange multiplier (λ) values and quantization parameter (QP) values to determine the cost function when a number of bits per section (NBS) of the digital picture is in a predetermined range and determined using a default relationship between the λ values and the QP values to determine the cost function otherwise. The determined cost function is used to make the section encoding mode decision and the section is encoded according to the encoding mode decision. It is emphasized that this abstract is provided to comply with the rules requiring an abstract that will allow a searcher or other reader to quickly ascertain the subject matter of the technical disclosure. It is submitted with the understanding that it will not be used to interpret or limit the scope or meaning of the claims.