The wavefront distortions produced by atmospheric fluctuations are discussed in this paper. The problem at hand is: What is the best way to process the measurements of these distortions so that appropriate corrections for them can be made? If a set of N independent wavefront measurements are made, the measured wavefront can be established as some linear combination of these measurements. The measurements themselves need not be direct phase measurements but could be a set of wavefront slope measurements. Nevertheless, the problem is to find a procedure that gives a best estimate of the wave-front from the set of N measurements. With such a procedure, the system designer can make an estimate of the number of measurements required to achieve a certain desired level of performance as well as the dynamical system complexity required to process the data. What is considered here is an application and adaptation of the theory of optimal estimates to the problem of random wavefront estimation.