Polymer blends that exhibit good impact resistance comprise a crystalline polypropylene matrix and a partly crystalline copolymer impact modifier with a molecular weight lower than that of the matrix polymer. The matrix polymer can comprise any crystalline propylene homo- or copolymer. The impact modifying copolymers are characterized as comprising at least about 60 weight percent (wt %) of units derived from propylene and, in certain embodiments, as having at least one, preferably two or more, of the following properties: (i) 13C NMR peaks corresponding to a regio-error at about 14.6 and about 15.7 ppm, the peaks of about equal intensity, (ii) a B-value greater than about 1.4 when the comonomer content of the copolymer is at least about 3 wt %, (iii) a skewness index, Six, greater than about −1.20, (iv) a DSC curve with a Tme that remains essentially the same and a Tmax that decreases as the amount of comonomer in the copolymer is increased, and (v) an X-ray diffraction pattern that reports more gamma-form crystals than a comparable copolymer prepared with a Ziegler-Natta (Z-N) catalyst.