  We calculate one-loop matching factors for bilinear operators composed of
improved staggered fermions. We compare the results for different improvement
schemes used in the recent literature, all of which involve the use of smeared
links. These schemes aim to reduce, though not completely eliminate, O(a^2)
discretization errors. We find that all these improvement schemes substantially
reduce the size of matching factors compared to unimproved staggered fermions.
The resulting corrections are comparable to, or smaller than, those found with
Wilson and domain-wall fermions. In the best case (``Fat-7'' and mean-field
improved HYP links) the corrections are 10 % or smaller at 1/a = 2 GeV.
