The aim of this paper is to present simple but efficient variance reduction methods for CONNFFESSIT-like simulations, extending the ideas of Hulsen et al. [J. Non-Newtonian Fluid Mech. 70 (1997) 79-101] and Ottinger et al. [J. Non-Newtonian Fluid Mech. 70 (1997) 255-261]. Strongly correlated local ensembles of dumbells were used, and equilibrium ensembles of dumbbells were subtracted. This idea is extended here to non-equilibrium ensembles of dumbbells. The methods are first presented in the frame of the plane Couette flow for Hookean and FENE dumbbells. Extensions to two-dimensional flows are discussed. (C) 1999 Elsevier Science B.V. All rights reserved.