Slush is made from a liquid using slush making systems or according to slush making processes. A jacketed vessel of the processes and the systems has an interior wall that defines an interior space. The interior space comprises a top and a bottom. The interior space has an average overall cross-sectional area taken through a vertical axis extending generally between the top and the bottom. The interior space also has a collection portion having an average collection portion cross-sectional area taken through the vertical axis that is less than the average overall cross-sectional area. The liquid is placed into the interior space and the interior walls are cooled. Slush forms on the interior walls and migrates to the collection portion. The collection portion is located at the interior space bottom when the slush density is higher than the liquid density and the collection portion is located at the interior space top when slush density is less than the liquid density. To facilitate the migration of the slush to the collection portion, at least a conical portion of the interior space has the general shape of a cone and the collection portion is located in the proximity of an apex of the conical portion, thereby helping to funnel the slush to the collection portion. The cryogenic liquid to be made into slush may be oxygen, nitrogen, hydrogen, helium, or water. The slush may be used to densify cryogenic liquids, such as cryogenic liquid propellants.