We consider the samples of a pure tone in additive white Gaussian noise (AWGN) for which we wish to determine the signal-to-noise ratio (SNR) defined here to be /spl alpha/=(A/sup 2//2/spl sigma//sup 2/), where A is the tone amplitude, and /spl sigma//sup 2/ is the noise variance. A and /spl sigma//sup 2/ are assumed to be deterministic but unknown a priori. If the variance of an unbiased estimator of /spl alpha/ is /spl sigma//sub /spl alpha//spl circ///sup 2/, we show that at high SNR, the normalized standard a deviation satisfies the Cramer-Rao lower bound (CRLB) according to /spl sigma//sub /spl alpha//spl circ////spl alpha//spl ges//spl radic/(2/N), where N is the number of independent observables used to obtain the SNR estimate /spl sigma//spl circ/.