In transmission and receiver design for radar or communication systems whose noisy channels contain Gaussianly fluctuating multipath, it is convenient to adopt a receiver output signal-to-noise ratio (SNR) criterion even though best error performance is actually sought. We investigate the loss (expressed as an equivalent transmitter output reduction) attending the use of this criterion. It is shown that when a Karhunen-Loeve analysis of the signaling system yields a largest eigenvalue that is suitably small, this loss is minor or negligible at all levels of error probability. Furthermore, it is easily possible to have a channel-perturbed transmission that is sufficiently weak and incoherent for this eigenvalue to guarantee low loss, yet not so weak that high output SNR (good error performance) is precluded.