It is shown that by drawing multiple samples from $N(\mu_i, \sigma^2_i) = 1, 2)$ it is possible to have confidence interval of preassigned length for the Behrens-Fisher problem.
"Confidence Interval of Preassigned Length for the Behrens-Fisher Problem." Ann. Math. Statist. 38 (4) 1175 - 1179, August, 1967. https://doi.org/10.1214/aoms/1177698787