The synthesis of poly(3-hydroxbutyrate-co-4-hydroxybutyrate) is reported with a family of yttrium amine bis(phenolate) catalysts via ring-opening polymerisation of β-butyrolactone and γ-butyrolactone. Poly(3-hydroxybutyrate), poly(4-hydroxybutyrate) and poly(3-hydroxybutyrate-co-4-hydroxybutyrate) were prepared at −40 °C with a 10 mol L ⁻¹ monomer concentration using a range of amine bis(phenolate) catalysts. It was found that poly(3-hydroxybutyrate) synthesis is inferior under these conditions to that attainable at room temperature. In contrast, poly(4-hydroxybutyrate) synthesis achieved up to 33% conversion under these conditions. Poly(3-hydroxybutyrate) polymers containing up to 63% 4-hydroxybutyrate inclusion were obtained when β-butyrolactone and γ-butyrolactone were copolymerised, with γ-butyrolactone in excess in the monomer feed. The carbonyl resonances between 169 and 174 ppm in the ¹³C NMR spectra of this copolymer were assigned. Gel permeation chromatography of the copolymers showed that the number-average molecular weights are consistently greater than the calculated values, and the dispersities are generally greater than 1.4, demonstrating limited control by the catalysts. Despite this restricted control, these catalysts were able to convert appreciable amounts of monomers into polymers either individually or within a copolymerisation.