We present an adaptation of our previous fast, regularized parallel MRI reconstruction approach (LSQR-Hybrid) to encompass the reconstruction of partial-Fourier data. Reconstructions of partial-Fourier data require a constraint on the signal phase variation in the reconstructed image. Here, we employ a two-parameter Tikhonov regularization formulation to constrain the real and imaginary components separately. A variation of the LSQR-Hybrid algorithm is used to rapidly reconstruct a set of images across the two-dimensional regularization parameter search space. The “best” image available is chosen as the one with the least system error using the most regularization. Results are demonstrated with subsam