Optical holographic correlators can perform many correlations simultaneously. Because the output plane must be divided among the individual templates in the system, for many systems shift-invariance limits the number of correlation templates than can be stored in one correlator. When the system is completely shift-invariant, the correlation peak from one correlator can shift into an area that has been reserved for a different template; in this case, a shifted version of one object might be mistaken for a well-centered version of a different object. This paper describes a technique to control the shift-invariance of a correlator system by moving the holographic material away from the Fourier plane.