Methods for chilling a natural gas stream may comprise: obtaining an expanded natural gas stream from an outlet of an expander, in which the expanded natural gas stream has a lower temperature and pressure than does the natural gas stream; introducing at least a portion of the expanded natural gas stream to a heat exchanger to promote indirect thermal communication between the expanded natural gas stream or a portion thereof and an external refrigerant circulating through the heat exchanger by way of a cooling loop; obtaining a chilled natural gas stream from the heat exchanger; introducing the chilled natural gas stream to a cold separator; and obtaining from the cold separator a further chilled natural gas stream as an overhead stream. The cooling loop comprises at least one compressor, and the expander supplies at least a portion of the power needed to operate the at least one compressor.