Motion estimation is an essential processing step common to all Magnetic Resonance Elastography (MRE) methods. For dynamic techniques, the motion is obtained from a sinusoidal fit of the image phase at multiple, uniformly spaced relative phase offsets, φ, between the motion and the motion encoding gradients (MEGs). Generally, 4 to 8 uniformly spaced values of φ are used. We introduce a method, termed RME (reduced motion encodes), of reducing the number of relative phases required, thereby reducing the imaging time for an MRE acquisition. A frequency-domain algorithm was implemented using the Discrete Fourier Transform (DFT) to derive the general least-squares solution for the motion amplitude and phase given an arbitrary number of phase offsets. Simulation result shows that the noise level decreases as the number of φ increases. The decrease is largest when smaller numbers of φ are used and becomes less significant as the number increases. The minimum noise is obtained for a specific number, n, of φ when the phase is evenly distributed with interval π/n. Phantom studies show a similar trend with noise level. The resulting displacement images from different numbers of phase offsets are compared.