Stochastic simulation techniques, such as Brownian dynamics, provide us an extremely powerful tool for solving the usually nonlinear equations describing polymer dynamics in solutions and melts . However, the most challenging problems (e.g. the investigation of the universal behaviour of long polymer chains, or the ow calculation based on stochastic simulation techniques) in- volve a very large number of degrees of freedom and hence require an enormous amount of computer time. In order to solve such problems on currently available computers it is therefore necessary to develop strategies to drastically suppress the level of the uctuations in the simulations. The purpose of this note is to show that the recently proposed concept of Brownian con guration elds  in viscoelastic ow calculations can be regarded as an extremely powerful extension of variance! reduction techniques based on parallel process simulation.