This paper describes the molecular design of a speciality polyester for use as a fast-absorbable monofilament surgical suture. In the surgical context, fast-absorbable means tensile strength loss within a period of 10-14 days, the minimum period required for secure wound approximation, after which the suture gradually loses its mass integrity leading to complete mass loss within 2-3 months. In order to be fast-absorbable, it is necessary that the main monomer used in synthesizing the polymer is glycolide since the polymer repeating unit, -OCH2CO-, is the chemical structure which hydrolyses the most rapidly in the human body. However, glycolide alone would give a monofilament suture fibre which would be too stiff and unwieldy for practical purposes and so it needs to be copolymerised with other cyclic ester monomers such as L-lactide and caprolactone to modify its mechanical properties. In this way, a monofilament fibre can be obtained which has an appropriate balance of hydrolysability and flexibility. Thus, this work enters the realm of molecular engineering insofar that it involves the strict control of both the chemical and physical microstructure of the polymer during the synthesis and processing steps respectively. This paper will describe how this controlled molecular architecture can be achieved and some preliminary results will be presented.