We compute the two-loop enhancement factors for our earlier one-loop
calculations of leading (1/Q) power corrections to the mean values of some
event shape variables in deep inelastic lepton scattering. The enhancement is
found to be equal to the universal ``Milan factor'' for those shape variables
considered, provided the one-loop calculation is performed in a particular way.
As a result, the phenomenology of power corrections to DIS event shapes remains
largely unaffected.Comment: 15 pages, 1 figure, uses JHEP.cls. This revised version corrects an
error in the calculation of the enhancement factor. The main conclusions
remain unchange