This paper presents the report of investigations ona prioriapodization of the pupil of a telescope operating in a turbulent medium. The criterion of apodization has been taken to be the maximization of the factor of encircled energy on a pre-specified area on the far-field plane. It has been observed that the optimum pupil function designed on the basis of a perfectly space-coherent wave being incident on the pupil has got to be modified by a small but significant amount to obtain the optimum function when a partially space-coherent wave is incident on the same. This leads to the possibility of using turbulence-corrector pupils in conjunction with the optimum pupil function designed for the coherent case to achieve an overall apodization. Numerical results are presented.