Dynamic viscoelasticity and dynamic birefringence were investigated for a series of polyesters with various combinations of dimethyl decalin 2,6-carboxylate, DMHN and dimethyl terephthalate, DMT as acid component and 9,9-bis[4-(2-hydroxy-ethoxy)phenyl]fluorene, BPEF and ethylene glycol, EG as diol component. The lowering of the stress-optical coefficient was achieved by the displacement of phenylene (DMT) with a hydrogenated naphthylene ring (DMHN) in the main chain and by the introduction of BPFE in the place of EG. The former choice lowered the intrinsic birefringence but did not affect the chain flexibility. The latter enhanced the flexibility but did not affect the intrinsic birefringence. The systematic result clearly revealed the importance of two different factors, the anisotropy of structural units and the chain flexibility, in molecular designs for polymers with low stress-optical coefficient.