We present results of the careful study of the Gribov copies problem in SU(
2) lattice gauge theory for the direct maximal center projection widely use
d in confinement studies. Applying simulated annealing algorithm we demonst
rate that this problem is more severe than it was thought before. The proje
cted (gauge noninvariant) string tension is not in the agreement with the p
hysical string tension, We do not find any indications that P-vortices repr
oduce the full SU(2) string tension neither in the infinite volume limit no
r in the continuum limit. (C) 2001 Published by Elsevier Science B.V.