By means of simple numerical examples it is demonstrated how the value of coefficient alpha is determined by the size and sign of the item intercorrelations, the dimensionality of the items, and the number of items. Relatively high alphas may be obtained for multidimensional item data (as obtained under a violation of essential tau-equivalence). Dimensionality analyses should therefore precede internal-consistency analyses if unidimensional tests are required. Such analyses also may alert one to the possibility of negative alpha values. Alternative coefficients are mentioned for situations when essential tau-equivalence is in doubt.