Thermal compression fluctuations of a long molecule, like DNA, are accounted when a bead is attached to the end of the molecule. When the bead is acted by some trapping (attractive) potential produced, for example, by optical tweezers, this potential can be essentially renormalized due to compression thermal fluctuations of the long molecule. The effective potential may turn over into a repulsive one for a sufficiently long molecule. The effect should be taken into account for an analysis of bead fluctuations. (C) 2003 American Institute of Physics.