Two concepts of particular relevance for educational and psychological measurement research using the popular structural equation modeling methodology are revisited—saturated model and (just) identified model. The distinction is emphasized between a saturated model on the one hand and an identified model on the other. It is shown that a saturated model need not be identified (and thus need not be just identified). Within that context, it is stressed that for a given set of observed variables there may be more than a single saturated model. To avoid possible confusion, a proposal is made to use the concept of “the saturated model” as referring only to the model with unconstrained variances, covariances, and means for a given set of manifest measures and to make references to “a saturated model” whenever any of the possible set of saturated models for these observed variables is meant.