A propylene copolymer is described comprising at least 70 mol % of units derived from propylene, up to 30 mol % of units derived from a combination of ethylene, at least one alpha-olefin having from 4 to 10 carbon atoms, such that the molar ratio of ethylene-derived units to said alpha-olefin-derived units in said combination is from about 1:9 to about 9:1, and from 0 to about 3 mol % of units derived from a copolymerizable diene. The copolymer has isotactically arranged propylene derived sequences, an overall heat of fusion as determined by differential scanning calorimetry (DSC) of less than 65 J/g, a second melting point as determined by DSC of less than 100° C., less than one 1,3 insertion error per 1000 carbon atoms and a weight average molecular weight as determined by gel permeation chromatography (GPC) of from about 100,000 to about 500,000.