Increasing the size of the ensemble used in hybrid-variational assimilation methods has been shown to be beneficial, but is computationally expensive. This work sets out to see whether similar improvements can be obtained from a smaller ensemble by better estimation of ensemble covariances. Methods for improving these are described and illustrated using a toy model. The optimal settings depend on the ensemble size, the criterion used to measure error and the errors in ensemble generation. A hybrid covariance, filtered by spectral localization using wavebands and scale-dependent spatial localization, is shown to perform well and robustly. In the cycled ensemble data-assimilation scheme used for numerical weather prediction (NWP), another method of increasing the effective ensemble size in covariance estimates is the use of time-lagged and time-shifted perturbations. This is demonstrated to be effective in the Met Office's hybrid-4DEnVar system, both on its own and with waveband and scale-dependent localization. The best such combination performs nearly as well as an increase in ensemble size from 44 to 200.