Disclosed are oxygen-scavenging polymer compositions having high transparency and low haze comprising immiscible blends of at least one polyester comprising 2,2,4,4-tetramethyl-1,3-cyclobutanediol, a copolyamide or a transamidized, homogeneous blend of a least two polyamides, and a metal catalyst. The components of the immiscible blend which have refractive indices which differ by about 0.006 to about −0.0006. The small difference in the refractive indices enable the incorporation of regrind into the polymer composition to produce transparent shaped articles. The blends of the present invention are useful in producing shaped articles such as, for example, sheeting, films, tubes, bottles, preforms and profiles. These articles may have one or more layers and can exhibit improved excellent barrier properties and good melt processability while retaining excellent mechanical properties.