A reduced rank Kalman filter has been developed and tested in the context of the 4D-Var data assimilation system at ECMWF. The RRKF modifies the 4D-Var background constraint by propagating covariances within a small subspace, according to the Kalman filter equations. The subspace can be defined either by a set of Hessian singular vectors, or as a balanced-truncation subspace, as proposed by Farrell and Ioannou (2001). It is demonstrated that the RRKF is beneficial in the context of a low resolution, quasi-geostrophic model. However, no significant benefit was apparent, for affordable subspace size, when the method was applied to a high resolution NWP system.