Clouds in the Arctic differ from clouds elsewhere in that they have a net warming effect at the surface. This happens because the longwave (LW) radiation dominates the radiation regime due to large solar zenith angles throughout the year, combined with a high surface albedo. We have looked at how an increased amount of anthropogenic sulfate aerosols in Arctic clouds can modify the radiation budget in the region. In doing this we used both a one dimensional model based on the NCAR CCM3 radiation scheme and the three dimensional CAM-Oslo climate model. An increased amount of sulfate aerosols alters the clouds mainly through the first and the second indirect effect giving them smaller effective drop radii and higher liquid water paths. Elsewhere on Earth this would lead to an increased cooling effect, but given the LW dominance and the optically thin clouds in the Arctic it has been suggested that the change may lead to an increased warming by the clouds in this region. Studies by Garrett and Zhao (2006) and Lubin and Vogelmann (2006) have under certain conditions found an increase in the LW surface flux on the order of 3.3 to 8.2 W/m^2 due to indirect effects. We have studied these effects by using present and pre-industrial emission scenarios as well as a scenario with increased SO_2 emissions compared to present day. Our results suggest that cloud forcing is less susceptible to increased levels of pollution today than it was pre-industrially. The reduced sensitivity is caused by large amounts of aerosols already available to the clouds in present day. The increased aerosol levels from pre-industrial times until today leads to an annually averaged increase in the LW cloud forcing at the surface of 0.64 W/m^2. Although these simulated results are subject to uncertainties, the overall importance of the increase in LW surface flux seems significantly lower than the maximum possible increase in this quantity found in earlier studies. The annually averaged change in SW cloud forcing with indirect effects is -0.99 W/m^2, while the simulated net change in surface cloud forcing due to anthropogenic aerosols averages to -0.35 W/m^2. Due to LW dominance in winter, the average change in cloud forcing from October to May is positive (0.2 W/m^2), while the change in forcing averaged over the remaining months is negative (-1.4 W/m^2). We conclude that the overall effect of increased levels of anthropogenic sulfate aerosols under cloudy skies is a small decrease in the surface radiative flux.