Transient stability analysis is becoming increasingly important for power systems engineers and researchers. Accurate dynamic models are required, but aggregate load models are an area of weakness. Measurement-based system identification methods based on least-square minimization have difficulty determining model parameters because the models do not satisfy injectivity: vastly different model parameters can produce the same output waveform for a given disturbance. One could argue that the parameters of a model are unimportant, as long as the simulation output waveforms are correct. While this is true for the disturbance(s) we used to determine the parameters, we show that the model fails when we try to use it to predict the result of other disturbances. Thus, we must attempt to regain injectivity. In this paper, we present two methods for doing so. First we try using multiple disturbances, but this does not have a significant impact. Second, we present an algorithm based on a maximum a-posteriori (MAP) estimator, which is much more robust than least-squares. The MAP estimator can take advantage of prior knowledge of the parameters of the grid. When we know a great deal about the model parameters beforehand, the MAP estimator is extremely robust to measurement noise, even down to SNRs approaching zero. When we do not, even if we simply guess that each of the five components in the complex load model comprises 20% of the total load, the MAP estimator still performs significantly better than least squares.