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The false (sideband) lock problem in Shuttle Costas loop receivers, in the presencse of noise, is assessed in this paper. False lock margin is defined depending on symbol signal-to-noise ratio rather than in the absence of noise as reported earlier in , . Closed form results are given when the arm filters of the Costas loop are one-pole Butterworth filters as used in the Shuttle receivers. However, the approach taken is also general enough to cover filters of arbitrary characteristics. As part of the development of the false lock margin, it is shown that the false lock phenomenon of the squaring loop is identical to that of the Costas loop.