  We analyze previously proposed order parameters for the confinement -
deconfinement transition in lattice SU(2) Yang-Mills theory, defined as vacuum
expectation value (v.e.v.) of monopole fields in abelian projection gauges. We
show that they exhibit some inconsistency in the treatment of small scales, due
to a violation of Dirac quantization condition for fluxes. We propose a new
order parameter avoiding this inconsistency. It can be interpreted as v.e.v. of
the field of a regular monopole in any abelian projection gauge, but it is
independent of the choice of the abelian projection. Furthermore, being
constructed in terms of surfaces of center vortices, it has also a natural
interpretation in the approach of center dominance.
