A parametric mean length is defined as the quantity (The equation is abbreviated), where R>0 (6≠1), Σpi=1. This being the useful mean length of code words weighted by utilities, u(subscript i). Lower and upper bounds for (subscript Rβ) RL(subscript u) are derived in terms of 'useful'-R-norm information measure for the incomplete power distribution, p(superscript β).