Multichannel regression algorithms are widely used in retrievals of sea surface temperature (SST) from infrared brightness temperatures (BTs) observed from satellites. The SST equations typically include terms dependent on the difference between BTs observed in spectral bands with different atmospheric absorption. Such terms do account for variations in the variable atmospheric attenuation, but may introduce additional noise in the retrieved SST due to amplification of the radiometric noise. Some processing systems (e.g., the EUMETSAT OSI-SAF) incorporate noise suppression algorithms, based on spatial smoothing of the differential terms in the SST equations. A similar algorithm is being tested for the potential use in the NOAA Advanced Clear-Sky Processor for Oceans (ACSPO). The ACSPO smoothing algorithm aims to preserve natural variations in SST field, while minimizing distortions in the original SST imagery, at a minimal processing time. This presentation describes the ACSPO smoothing algorithm and results of its evaluation with the SST imagery, and with the in situ matchups for NOAA and Metop AVHRRs, Terra and Aqua MODISs, and SNPP/JPSS VIIRS.