Noise correlations exist in multi-channel k-space data, and methods to optimally account for this correlation have been used for a long time in image-domain parallel imaging methods like SENSE. However, methods to address noise are not widely-utilized for Fourier-domain parallel imaging methods like GRAPPA, SPIRiT, and AC-LORAKS. In this work, we demonstrate that properly accounting for spatially-varying noise correlation can substantially reduce the noise level of coil-combined images. Further, we demonstrate the existence of previously-unknown correlations between the real and imaginary parts of the noise in reconstructed images. Accounting for this extra correlation can reduce the noise level even further.