Suture-specific coatings having a number average molecular weight not exceeding 20 kDa, a melting temperature above 37° C., and heat of fusion exceeding 20 J/g, are formed of copolyesters of polycaprolactone or of ε-caprolactone and at least one cyclic monomer forming a segmented polyester chain initiated by a polyaxial crystalline organic compound or an amorphous polyaxial polymeric initiator and include from about 0.01 to about 10 weight percent of at least one molecularly dispersed bioactive agent.