The authors explore likelihood-based methods for making inferences about the components of variance in a general normal mixed linear model. In particular, they use local asymptotic approximations to construct confidence intervals for the components of variance when the components are close to the boundary of the parameter space. In the process, they explore the question of how to profile the restricted likelihood (REML). Also, they show that general REML estimates are less likely to fall on the boundary of the parameter space than maximum-likelihood estimates and that the likelihood-ratio test based on the local asymptotic approximation has higher power than the likelihood-ratio test based on the usual chi-squared approximation. They examine the finite-sample properties of the proposed intervals by means of a simulation study.