Copolymers of ethylene glycol with 4,4'-bibenzoic acid and terephthalic acid are known to crystallize rapidly to surprisingly high levels of crystallinity. To understand this unusual behavior, the isothermal crystallization of poly(ethylene bibenzoate-co-terephthalate) in the molar ratio 55:45 (PETBB55) was studied. Poly(ethylene naphthalate) (PEN) was included in the study for comparison. The kinetics of isothermal crystallization from the melt and from the amorphous glass was determined using differential thermal analysis. The results were correlated with the crystalline morphology as observed with atomic force microscopy (AFM). Crystallization of PEN exhibited similar kinetics and spherulitic morphology regardless of whether it was cooled from the melt or heated from the glass to the crystallization temperature. The Avrami coefficient was close to 3 for heterogeneous nucleation with 3-dimensional crystal growth. The copolymer PETBB55 crystallized much faster than did PEN and demonstrated different crystallization habits from the melt and from the glass. From the melt, PETBB55 crystallized in the "normal" way with spherulitic growth and an Avrami coefficient of 3. However, crystallization from the glass produced a granular crystalline morphology with an Avrami coefficient of 2. A quasi-ordered melt state, close to liquid crystalline but lacking the order of a recognizable mesophase, was proposed to explain the unusual crystallization characteristics of PETBB55.