Disclosed is a process for the preparation of shaped articles such as, for example, sheeting, films, tubes, bottles, preforms and profiles, having high transparency and low haze, and comprising immiscible blends of at least one polyester comprising 2,2,4,4-tetramethyl-1,3-cyclobutanediol, and a copolyamide or a transamidized, homogeneous blend of a least two polyamides. The components of the immiscible blend 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. These articles may have one or more layers and can exhibit improved excellent barrier properties and good melt processability while retaining excellent mechanical properties. Metal catalysts can be incorporated into the compositions to produce shaped articles having oxygen-scavenging properties.