When performing multi-component significance tests with multiply-imputed datasets, analysts can use a Wald-like test statistic and a reference F-distribution. The currently employed degrees of freedom in the denominator of this F-distribution are derived assuming an infinite sample size. For modest complete-data sample sizes, this degrees of freedom can be unrealistic; for example, it may exceed the complete-data degrees of freedom. This paper presents an alternative denominator degrees of freedom that is always less than or equal to the complete-data denominator degrees of freedom, and equals the currently employed denominator degrees of freedom for infinite sample sizes. Its advantages over the currently employed degrees of freedom are illustrated with a simulation. ©2007 Biometrika Trust.