This paper shows that if one designs an LQG controller using the conventional technique of loop transfer recovery (LTR), then two frequency weighted controller reduction methods, the Enns' frequency weighted balanced truncation (Enns, 1984a, Ph.D. Thesis, Stanford University, CA; 1984b, Proc. 23rd CDC, Las Vegas, NV, 127–132) and the Bezout identity induced frequency weighted reduction method (Anderson and Liu, 1987, Proc. Amer. Control Conf., MN) will be equivalent under the condition that the plant transfer function is square, nonsingular and minimum phase. We also show that Enns' method is equivalent to the Bezout identity induced frequency weighted reduction method if the controller itself is stable and a particular representation for the controller is assumed.