An extensible fiber comprising a propylene copolymer has been patented. The copolymer comprises at least about 50 weight percent of units derived from propylene and at least about 5 weight percent of units derived from a comonomer other than propylene. The fiber is characterized as having a crystallinity index less than 30% and a modulus of less than or equal to about 22 g/den. The extensible fiber can be characterized by having a retained load of more than or equal to about 2.5% and an immediate set of less than or equal to about 22% as determined in a 50% 1-cycle test. The 50% 1-cycle test is one in which a load on the fiber is measured while the fiber is extended at a rate of 10 inches per minute to an elongation of 50% then retracted to an elongation of 0% at a rate of 10 inches per minute and then extended a second time to an elongation of 50% at a rate of 10 inches per minute. The retained load is the load measured at 30% elongation during retraction divided by the load measured at 30% elongation during the first extension. The immediate set is the elongation at which a positive load is first measured during the second extension.