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We consider a construction of approximate confidence intervals on the variance component ${\sigma }_1^2$ in mixed linear models with two variance components with non-zero degrees of freedom for error. An approximate interval that seems to perform well in such a case, except that it is rather conservative for large ${\sigma }_1^2/{\sigma }^2,$ was considered by Hartung and Knapp in [hk]. The expression for its asymptotic coverage when ${\sigma }_1^2/{\sigma }^2\to \infty$ suggests a modification of this interval that preserves some nice properties of the original and that...