The micro-macro simulations of polymeric fluids couple the mass and momentum conservation equations at the macroscopic level, with a stochastic differential equation which models the evolution of the polymer configurations at the microscopic level (Brownian dynamics simulation). Accordingly, the system is discretized by a finite element method coupled with a Monte Carlo method. All the discrete variables are random, and the accuracy of the result highly depends on the variance of these random variables. We give here some elements of numerical analysis on the crucial issue of variance reduction in order to get results of a better quality for a given computational cost. The present analytical study only deals with a one-dimensional case, but nevertheless gives a track for computational strategies that may apply to the more physically relevant two- and three-dimensional cases. (C) 2004 Elsevier B.V. All rights reserved.