A method for cryogenic cooling without fouling is disclosed. The method comprises providing a first cryogenic liquid saturated with a dissolved gas; expanding the first cryogenic liquid into a separation vessel, separating into a vapor, a second cryogenic liquid, and a first solid; drawing the vapor into a heat exchanger and the second cryogenic liquid and the first solid out of the separation vessel; cooling the vapor against a coolant through the heat exchanger, causing the vapor to form a third cryogenic liquid and a second solid, the second solid dissolving in the third cryogenic liquid; and combining the second cryogenic liquid and the first solid with the third cryogenic liquid, producing a final cooled slurry. In this manner, the cryogenic cooling is accomplished without fouling.