We present a new approach for estimating the parameters of three-phase untransposed electrically short transmission lines using voltage/current synchrophasor measurements obtained from phasor measurement units. The parameters to be estimated are the entries of the longitudinal impedance matrix and the shunt admittance matrix at the rated system frequency. Conventional approaches relying on the admittance matrix of the line cannot accurately estimate these parameters for short lines, due to their high sensitivity to measurement noise. Our approach differs from the conventional ones in the following ways: First, we model the line by the three-phase transmittance matrix that is observed to be less sensitive to measurement noise than the admittance matrix. Second, we compute an accurate noise covariance matrix using the realistic specifications of noise introduced by instrument transformers and phasor measurement units. This noise covariance matrix is then used in least-squares-based estimation methods. Third, we derive different least-squares-based estimation methods based on a statistical model of estimation and show that the weighted least-squares and the maximum likelihood methods, which make use of the noise covariance matrix produce the best estimates of the line parameters. Finally, we apply the proposed methods to a real dataset and show that our approach significantly outperforms existing ones.