Estimates published between 1975 and 1997 of mass, heat, and salt fluxes into and out of the Arctic Basin are statistically combined into aggregate estimates for the purpose of determining the uncertainty of the budgets. Because they include information from many previous estimates, the aggregate estimates are consistent with previous results but with smaller uncertainty. The sums of the aggregate estimates are nonzero but within two standard errors of zero. Systematic adjustment of the aggregate estimates in proportion to their uncertainties gives two new sets of flux estimates: one set that conserves volume (as an approximation to mass), and another that conserves volume, heat, and salt. The conservation requirements greatly reduce the uncertainty of the most uncertain terms in the budgets. The budgets indicate the necessity, in steady state, of a net average flux of 1.4¿0.3¿106 m3 s-1 from the Arctic shelves to the Arctic basin, consistent with previous estimates. The budgets also imply a net freshwater flux from the shelves into the basins: the freshening effect of surface transport is larger than the salinating effect of dense shelf overflows. The uncertainties derived here are lower-bound estimates as they do not consider the effects of aliasing or other undersampling errors. ¿ 1999 American Geophysical Union