An index describing the sharpness of glass transitions is proposed in this work. This index is closely connected to thermoplasticity, which was determined as the slope of logarithmic storage modulus (log E')-temperature curves, that is, -d log E'/dT at a point just above the T-g determined by dynamic mechanical analysis (DMA). The main purpose of this work was to obtain high-temperature polymeric materials while simultaneously achieving low coefficients of thermal expansion (CTE < 20 ppm K-1) and excellent thermoplasticity with higher indices (-d log E'/dT > 0.3) as an empirical benchmark without rubbery plateau (RP) regions in the DMA curves. However, it was very difficult to accomplish this goal because of the presence of a clear trade-off between lower CTE and higher thermoplasticity as observed in common polymer systems. Therefore, we designed a series of diamines incorporating benzoxazole (BO) units to develop novel poly(benzoxazole imide)s (PBOIs) with the expectation of weakening the intermolecular forces present in the systems by decreasing the amount of imide C=O groups. The combination of an ether-linked BO-incorporating diamine and a rigid tetracarboxylic dianhydride led to a PBOI with somewhat improved thermoplasticity and a significantly decreased CTE, however, it was difficult to completely remove the RP regions. On the other hand, a meta-phenylene-linked BO-incorporating diamine was effective in erasing the RP regions with a considerably high index (-d log E'/dT - 0.60) while keeping a relatively low CTE. This system was modified by copolymerization with a minor fraction of a p-linked BO-incorporating diamine. The resultant copolymer attained a low CTE (16.7 ppm K-1) close to that of copper foils and a high index (-d log E'/dT = 0.37) without RP regions. A reasonably high adhesion strength was also observed for the hot-compressed laminates between the copolymer film and copper foils. The copolymer prepared possessed a very high T-g of 362 degrees C, sufficient ductility, a relatively low water uptake of 1.57%, and the highest rank of non-flammability. Thus, the PBOIs developed in this work offer useful materials for potential applications as adhesive-free flexible printed circuits. (C) 2016 Elsevier Ltd. All rights reserved.