The present invention provides a constant release copolymer composition adapted for use in a controlled release formulation for a bioactive agent, such as a formulation adapted for implantation within a patient's body tissues as a depot to release the agent over a period of time, wherein the copolymer provides a substantially constant rate of release of the bioactive agent over the time period for which the depot persists in the body tissues. The copolymer includes a PLG copolymer and a PLG oligomer of about 5-10 kDa average molecular weight, which can lack free carboxylic acid groups. When the PLG copolymer is a low burst copolymer, the constant release copolymer composition is a low burst, constant release copolymer composition adapted for implantation in the body tissues of a mammal, wherein a substantially constant rate of release of the bioactive agent is achieved.