<p>We derive a mode basis of aberration components of the Kolmogorov wavefront. The basis is characterized by the maximum contribution to the geometric transverse aberration of a uniformly intense circular monochromatic laser beam. The result represents the Karhunen—Loève functions derived from the Lukosz polynomials. With modal successive correction, subtraction of these components from the wavefront results in the strongest decrease of the RMS focal spot radius, allowing for statistical improvement of the focusing effect of laser radiation. The result obtained within the geometric optics approximation is also valid for the diffraction focal spot. Results of numerical simulation show that the characteristic focal spot size depending on the turbulence level can be reduced by several percent or tens of percent, while the Strehl ratio and the power in the bucket can be increased from several percent to more than a hundred percent (as compared to the modal correction of the same number of the known aberration components). It is also proposed to use modified Karhunen—Loève functions as aberration components, which in most cases allow for higher focusing parameters than those with the newly derived Karhunen—Loève—Lukosz modes. These results can be generalized for any given model of atmospheric phase distortions, an arbitrary aperture shape, and a given laser beam apodization.</p>