The principal phenomena limiting an accuracy of laser beaming of remote objects in atmosphere is the atmospheric turbulence that induces the laser beam wandering over the object. Recently, a novel algorithm, which is referred as "a bright speckle algorithm", was proposed to compensate for wandering of a repetitively pulsed laser beam, propagating along at the atmosphere range. In the paper we consider the restrictions on the algorithm performance, which are imposed by the atmospheric turbulence. The restrictions are imposed on a distance range of the algorithm as well as on coincidence accuracy of the probe and operation beam wavefront profiles, which are used for the algorithm realization.