A method for forming a biodegradable aliphatic polyester suitable for use in fibers is provided. In one embodiment, for example, an aliphatic polyester is melt blended with an alcohol to initiate an alcoholysis reaction that results in a polyester having one or more hydroxyalkyl or alkyl terminal groups. By selectively controlling the alcoholysis conditions (e.g., alcohol and polymer concentrations, catalysts, temperature, etc.), a modified aliphatic polyester may be achieved that has a molecular weight lower than the starting aliphatic polyester Such lower molecular weight polymers also have the combination of a higher melt flow index and lower apparent viscosity, which is useful in a wide variety of fiber forming applications, such as in the meltblowing of nonwoven webs.