Conventional random-effects models in meta-analysis rely on large sample approximations instead of exact small sample results. While random-effects methods produce efficient estimates and confidence intervals for the summary effect have correct coverage when the number of studies is sufficiently large, we demonstrate that conventional methods result in confidence intervals that are not wide enough when the number of studies is small, depending on the configuration of sample sizes across studies, the degree of true heterogeneity and number of studies. We introduce two alternative variance estimators with better small sample properties, investigate degrees of freedom adjustments for computing confidence intervals, and study their effectiveness via simulation studies.