We show experimentally and theoretically that the heliconical fluctuations that develop in a cholesteric phase (Ch) close to a transition to a chiral twist-bend nematic phase (N_{TB}) may lead to the appearance of a compensation point. At this point, the equilibrium twist of the cholesteric phase vanishes and changes sign. Mixtures of the flexible dimer CB7CB and the rodlike molecules 8CB or 5CB, doped with a small amount of the chiral molecules R811, S2011, CC, or CB15, are used in experiments to determine the conditions for the appearance of a compensation point.