The overidentification of structural equation models with latent variables is discussed. The use of two- and three-indicator models is not recommended since such models do not allow a testing of the crucial assumption of unidimensionality among indicators in most cases. Models with four or more indicators may be more sensitive to departures from unidimensionality among sets of indicators or an alleged common variable. Further, parsimonious models are to be preferred because they imply more observable consequences and more ways to be rejected, if false. Combining a parsimony index (James, Mulaik and Brett) with a normed fit index (Bentler and Bonnet) yields a normed parsimonious fit index. This combined index corrects for the tendency of the normed fit index to approach unity as the degrees of freedom of the model approach zero. Increasing the number of indicators, relative to the number of latent variables to be identified, can only serve to increase the parsimony of a model as long as the indicators are linked respectively to as few of the latent variables as possible. (PN)