The analysis of covariance (ANCOVA) is a useful statistical procedure that incorporates covariate features into the adjustment of treatment effects. The consequences of omitted prognostic covariates on the statistical inferences of ANCOVA are well documented in the literature. However, the corresponding influence on sample-size calculations for precise interval estimation has not been fully evaluated. This article aims to explicate the deficiency of approximate methods for ignoring the stochastic nature of covariate variables and to present exact approaches for precise interval estimation of treatment contrasts under the assumption that the covariate variables have a joint multinormal distribution. The desired precision of a confidence interval is assessed with respect to the control of expected half-width and to the assurance probability of interval half-width within a designated value. Numerical appraisals show that the suggested approaches outperform the approximate formulas for the two precision considerations.