What kind of tariff reform is likely to raise welfare in situations where tariff revenue is important? Uncertainty about specification and risk from imprecise parameter estimates of any particular specification reduce the credibility of simulation estimates. A promising alternative is to develop rules which are robust with respect to such uncertainty. We present sufficient conditions for a class of linear rules that guarantee welfare-improving tariff reform. The rules span cones of welfare-improving tariff reforms consisting of convex combinations of (i) trade-weighted-average-tariff-preserving dispersion cuts; and (ii) uniform tariff cuts that preserve domestic relative prices among tariff-ridden goods.