  We critically reconsider our recent observation of confining string shrinkage
in pure glue SU(2) lattice gauge theory near the continuum limit. Using the
advanced numerical techniques we argue that imperfect overlap with the string
ground state and corresponding ambiguities in T->\infty extrapolation are
likely to be the cause of the observed scaling violations. In particular, even
in the limit of large Euclidean times the string shrinkage is apparent in
torelon correlation function, however, in this case the best relevant overlap
we could attain is of order 50%. To the contrary, when the ground state is
selected properly the string width scales in physical units being ~0.3 fm for 1
fm long confining string.
