Reconstructed elastography maps suffer from noise due to derivative operations in the inversion algorithms. Considering the noise on the complex MRI signal, SNR of the reconstructed elastogram is derived analytically for k-MDEV inversion. Verified SNR derivations by Monte Carlo Simulations, an SNR-weighted k-MDEV inversion was proposed to maximize SNR of the elastogram. Quality of the proposed reconstruction was assessed by estimation error, noise performance and edge response analyses. SNR of the elasticity improved twice as the conventional method. Results on phantom and human liver data are also provided. As future work, this analysis will be performed for other inversion methods.