Ensemble data assimilation methods utilize ensembles of first-guess forecasts to estimate error statistics. The forecast error statistics are used to combine the first-guess forecasts with the observations to provide a set of analyses, which then provides initial states for the next ensemble forecast. In the ensemble Kalman filter (EnKF) the Kalman gain matrix, calculated using the ensemble error covariances, is used to blend the forecasts and observations. It has been shown that if the same gain matrix and the same observations are used to perform the analysis for each ensemble member, ensemble covariances will be systematically underestimated. To alleviate this problem, Burgers and Houtekamer have proposed assimilating ensembles of simulated observations whose statistics are consistent with observation error. In the limit of large ensemble size, this method produces the correct analysis statistics. However, for small ensembles the sampling error associated with the noise added to the observations can have deleterious effects on the analysis, particularly when simultaneous observations are assimilated serially. Recently, several ensemble data assimilation techniques have been proposed, including the ensemble adjustment and ensemble transform filters, which are able to obtain correct analysis statistics without adding noise to the observations. All of these methods are particular implementations of ensemble square-root filters. We utilize a particularly simple and efficient implementation of the square-root filter that is no more computationally expensive than the EnKF with perturbed observations when observations are assimilated serially, one at a time. The benefits of ensemble data assimilation without perturbed observations are demonstrated and interpreted using a hierarchy of models of varying complexity.