  Within the (dual) Abelian Higgs model, confining strings do not disappear at
small distances but rather become short strings. In compact 3D electrodynamics,
as we argue here, the confining strings are also manifested at small distances
in unusual power corrections, disobeying the standard rules of the Operator
Product expansion. In the most interesting case of QCD, there is yet no
derivation of short strings and we turn to phenomenology to find evidence pro
or contra their existence. The short strings in QCD lead to non-standard power
corrections. A tentative conclusion of the analysis of existing data, both in
numerical simulations and in real experiments, is that the novel power
corrections are present, at least at the mass scale of 1-2 GeV.
