In multistage refrigeration compression, where liquid refrigerant withdraw from a core-in-shell type heat exchanger connected to a high compression stage is passed to a similar exchanger connected to a lower compression stage, liquid level stability in the higher compression stage exchanger is improved by providing an enlarged surge volume. A baffle plate transversing a lower portion of the shell divides the shell into a cooling zone that contains the cores, and a discharge zone that is part of the surge volume. The height of the baffle is selected to facilitate maintenance of at least a minimum functional liquid level in the shell. Liquid refrigerant withdraw from the discharge zone of the high-stage shell is supplied to the cooling zone of a shell connected to a lower compression stage. The liquid level in the shell is maintained by manipulating flow to liquid refrigerant that is flashed into the cooling zone of the higher compression stage shell. A refrigerant compressor may employ two or more compression stages, where the higher stage shells are typically much smaller than the lower stage shells, and the described scheme prevent major liquid level upsets in the shell of a higher stage resulting from minor liquid level upsets in the lower stage shells.