Cohen [1] and Des Raj [2] have shown that in estimating the parameters of truncated type III populations, it is necessary to calculate for several values of $x$ the Mills ratio of the ordinate of the standardized type III curve at $x$ to the area under the curve from $x$ to $\infty$. Des Raj [3] has also noted that for large values of $x$ the existing tables of Salvosa [4] are inadequate for this purpose and he has found lower and upper bounds for the ratio. The object of this note is to improve these bounds, by obtaining monotonic sequences of lower and upper bounds through the use of continued fractions.