The European Centre for Medium-Range Weather Forecasts 45-year reanalysis (ERA-40) exhibits an enhanced Brewer-Dobson circulation, as is demonstrated for the year 1997 by examining the air mass transport across the 100-hPa level and the tropopause. On the basis of a linearized ozone (Linoz) scheme for stratospheric chemistry it is estimated that the corresponding net downward transport of ozone to the lowermost stratosphere and the troposphere would be a factor 2--3 too high. Different methods are evaluated to simulate the downward transport of stratospheric ozone in tropospheric chemistry transport models driven by ERA-40 meteorology. The synthetic ozone (Synoz) model, which is sometimes used to constrain the influx of stratospheric ozone by imposing its chemical production rate in the middle stratosphere, in the case of ERA-40 leads to an unacceptable depletion of the upper troposphere/lower stratosphere region, with nearly halved ozone concentrations at 100 hPa. A better alternative is to constrain the zonal mean concentrations in the lower stratosphere by relaxation to an ozone climatology. If ozone is relaxed down to 100 hPa in the extratropics, the net downward transport of ozone is reduced by more than a factor of 2. Finally, we investigate to what extent the circulation bias persists in the forecasts of the reanalysis. The use of forecasts beyond the 6-hour first guess in combination with relaxation yields a further reduction of the stratosphere-troposphere exchange of ozone, the 100-hPa flux approaching the range of observational estimates. An additional advantage of using forecasts is that the exchange of chemical constituents other than ozone is improved concurrently.