A method for cooling a hydrocarbon feed stream against a first refrigerant to produce a cooled hydrocarbon stream, the first refrigerant having a critical temperature, the method comprising: (a) compressing the first refrigerant in at least one compression stage to produce a compressed first refrigerant; (b) cooling the compressed first refrigerant against an ambient fluid in at least one heat exchanger to produce a cooled first refrigerant having a first temperature that is greater than or equal to the critical temperature of the first refrigerant; (c) further cooling the cooled first refrigerant in at least one economizer heat exchanger against at least a first portion of the cooled first refrigerant to produce a further cooled first refrigerant at a second temperature and a warmed first refrigerant, the second temperature being less than the critical temperature of the first refrigerant; and (d) cooling a fluid stream (601, 639) in each of at least one cooling circuit located in downstream fluid flow communication from the economizer heat exchanger, each of the at least one cooling circuit having at least one evaporation stage (681-684, 685-688), each of the following steps being performed in each evaporation stage: (i) reducing the pressure (673, 677) of the first refrigerant (622A, 661); (ii) cooling the fluid stream (601, 639) against the reduced pressure first refrigerant (620, 662) in an evaporator (681, 685), resulting in vaporization of at least a portion of the reduced pressure first refrigerant (621, 663); and (iii) flowing at least a portion of the vaporized reduced pressure first refrigerant into one of the at least one compression stages; wherein at least one fluid stream being cooled in the at least one cooling circuit comprises the hydrocarbon feed stream and step (d) produces a cooled hydrocarbon stream; characterized in that the method further comprises: (e) combining a vapor phase portion of the warmed first refrigerant with the vaporized reduced pressure first refrigerant in one of the at least one evaporation stage before performing step (d)(iii); and (f) separating the warmed first refrigerant into the vapor phase portion and a liquid phase portion and performing step (d) using the liquid phase portion. (a) compressing the first refrigerant in at least one compression stage to produce a compressed first refrigerant; (b) cooling the compressed first refrigerant against an ambient fluid in at least one heat exchanger to produce a cooled first refrigerant having a first temperature that is greater than or equal to the critical temperature of the first refrigerant; (c) further cooling the cooled first refrigerant in at least one economizer heat exchanger against at least a first portion of the cooled first refrigerant to produce a further cooled first refrigerant at a second temperature and a warmed first refrigerant, the second temperature being less than the critical temperature of the first refrigerant; and (d) cooling a fluid stream (601, 639) in each of at least one cooling circuit located in downstream fluid flow communication from the economizer heat exchanger, each of the at least one cooling circuit having at least one evaporation stage (681-684, 685-688), each of the following steps being performed in each evaporation stage: (i) reducing the pressure (673, 677) of the first refrigerant (622A, 661); (ii) cooling the fluid stream (601, 639) against the reduced pressure first refrigerant (620, 662) in an evaporator (681, 685), resulting in vaporization of at least a portion of the reduced pressure first refrigerant (621, 663); and (iii) flowing at least a portion of the vaporized reduced pressure first refrigerant into one of the at least one compression stages; (i) reducing the pressure (673, 677) of the first refrigerant (622A, 661); (ii) cooling the fluid stream (601, 639) against the reduced pressure first refrigerant (620, 662) in an evaporator (681, 685), resulting in vaporization of at least a portion of the reduced pressure first refrigerant (621, 663); and (iii) flowing at least a portion of the vaporized reduced pressure first refrigerant into one of the at least one compression stages; wherein at least one fluid stream being cooled in the at least one cooling circuit comprises the hydrocarbon feed stream and step (d) produces a cooled hydrocarbon stream; characterized in that the method further comprises: (e) combining a vapor phase portion of the warmed first refrigerant with the vaporized reduced pressure first refrigerant in one of the at least one evaporation stage before performing step (d)(iii); and (f) separating the warmed first refrigerant into the vapor phase portion and a liquid phase portion and performing step (d) using the liquid phase portion. (e) combining a vapor phase portion of the warmed first refrigerant with the vaporized reduced pressure first refrigerant in one of the at least one evaporation stage before performing step (d)(iii); and (f) separating the warmed first refrigerant into the vapor phase portion and a liquid phase portion and performing step (d) using the liquid phase portion.