The Wald statistic is frequently used to test hypotheses about beta coefficients from multiple linear regression analyses of complex survey data. This statistic requires a consistent estimate of the variance-covariance matrix of the regression coefficients. In a survey such as the Second National Health and Nutrition Examination Survey, the sample design limits the researcher to at most 32 degrees of freedom for estimating the variances and covariances with either the balanced half-sample replication or the Taylor series linearization procedure. This article considers the properties of the Wald statistic when the number of beta coefficients approaches the degrees of freedom available from the variance estimation. In this situation, Bonferroni-adjusted t statistics are an attractive alternative.