The signal-to-noise ratio (SNR) of the optical heterodyne beat between a low-power laser and an optical frequency comb with a relatively low mode power is often insufficient to exclude the possibility of frequency counter error. We develop some methods to enhance this beat SNR including the adoption of a fiber coupler, the suppression of the shot noise, and the utilization of Ti:sapphire laser output. We obtain the highest SNR ever reported with similar laser systems by these methods. With sufficiently enhanced SNR, we measure the absolute frequency of some optical frequency standards without counter error. We give some experimental criteria of beat SNR for the correct frequency count.