The present disclosure relates to propylene-ethylene copolymers comprising an ethylene content of 0.1-10% by weight, a molecular weight distribution (MWD), expressed in terms of Mw/Mn, of greater than 3.0 and a xylene soluble (XS) fraction content defined by values that fall below the line given by the equation XS=1.0296·e0.435C2. The propylene-ethylene copolymers advantageously exhibit high transparency and low melting temperatures.