Strain Encoded Magnetic Resonance Elastography (SENC MRE) has been proposed for imaging elastic variation by obtaining images whose intensity directly: represents through-plane strain. It is useful for detecting tumors because tumors exhibit different elastic properties than the surrounding tissue. SENC MRE, however, assumes homogeneous tissue elasticity in the through-plane direction, an assumption that requires the acquisition of relatively thin image slices. This causes a reduction in the signal-to-noise-ratio (SNR) of the images and lengthens the scanning time when acquiring large volumes. In this paper, we evaluated imaging with thick slices (>10 mm) where the homogeneity assumption would fail in cases of small tumors that are thinner than the image slice. We propose enhancing the SENC MRE technique to detect thin tumors by modifying the image slice profile. Phantom experiments were performed to demonstrate the ability of the improved SENC MRE technique to detect the presence of thin tumors, as small as one quarter of the slice thickness.