We show that for magnetic resonance (MR) images with signal-to-noise ratio (SNR) less than 2 it is advantageous to use a phase-corrected real reconstruction, rather than the more usual magnitude reconstruction. We discuss the results of the phase correction algorithm used to experimentally verify the result. We supplement the existing literature by presenting closed form expressions (in an MR context) for the probability distribution and first moments of the signal resulting from a magnitude reconstruction.