We consider a construction of approximate confidence intervals on the variance component $\sigma^2_1$ 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 $\sigma^2_1/\sigma^2,$ was considered by Hartung and Knapp in \cite{hk}. The expression for its asymptotic coverage when $\sigma^2_1/\sigma^2\rightarrow\infty$ suggests a modification of this interval that preserves some nice properties of the original and that is, in addition, exact when $\sigma^2_1/\sigma^2\rightarrow\infty.$ It turns out that this modification is an interval suggested by El-Bassiouni in \cite{eb}. We comment on its properties that were not emphasized in the original paper \cite{eb}, but which support use of the procedure. Also a small simulation study is provided.