The current invention is concerned with block copolyesters of low glass transition temperature segments and ethylene glycol based polyester segments linked together by carboxylic acid ester groups and special diols, and a process for preparing these copolyesters. These copolyesters display molded resin properties similar to polyethylene terephthalate but crystallization behavior similar to polybutylene terephthalate, i.e. they have high strength and superior solvent resistance, but they also crystallize rapidly. They are made by subjecting low glass transition temperature (less than 0.degree. C.) polymers with carboxyl, hydroxyl or reactive ester end groups to esterification or transesterification conditions with ethylene glycol based polyester segments having a minimum intrinsic viscosity of 0.2 dl/g and special diols having four to ten carbon atoms with 3 or 4 carbon atoms between the hydroxyl groups in the presence of appropriate catalysts. In a preferred embodiment, the three components are subject to melt homogenization in an extruder and the solidified extrudate is subject to a solid state polycondensation reaction.