The efficiency of tracking the random tilt variation of the wavefront in order to increase the average intensity with possible suppression of the intensity fluctuations is investigated. The analysis of the subject is suitable for both transmitting and receiving optical systems. The suggestion of a simple approximation for the tilt-corrected phase structure function allows us to reduce the integration order in the expressions for the statistical moments of the corrected field and to express them in the same form as those in the absence of the correction. Comparison of the results for arbitrary efficiency criteria of the correction demonstrates that the optimal conditions for fluctuation suppression and the increase of the average intensity at the recording point occur in different turbulent regimes. A significant fluctuation suppression is observed at a much weaker turbulence level as compared with the value corresponding to the maximum of the average intensity increase.