Fast hydrolyzable polyesters are promising candidates as biodegradable plastics degrading to carbon dioxide, water, and biomass in the presence of oxygen in a suitable environment. The rate-determining step of biodegradation is the fragmentation of polyesters to lower mass fragments by hydrolysis, which in the second step undergo bioassimilation. Polyesters with a balance of good mechanical properties and fast hydrolyzability are urgently needed as a sustainable solution to the problem of plastic pollution and persistent microplastics when used in packaging and agricultural applications. Aromatic polyesters, such as poly(butylene terephthalate) (PBT), are mechanically strong but require harsh hydrolysis conditions, making them nonbiodegradable. The trend is mostly the opposite for aliphatic polyesters. We present in this work an aromatic polyester, a constitutional isomer of PBT [poly(1,4-benzenedimethylene succinate) (PBDMS)], and its copolymers (PB x BDM y S) in which aliphatic ester units balance the mechanical, thermal, and hydrolysis properties. PBDMS was prepared from 1,4-benzenedimethanol (BDM) and succinic acid (S) via two-step polycondensation. Its copolyesters with 1,4-butanediol (B) as a comonomer are also presented. High-molecular-weight PBDMS showed a glass-transition temperature of 6 °C and a melting temperature around 100 °C, very high thermal stability, and melt processability. The structure−property relationship of such polyesters was intensively studied, focusing on the impact of molecular composition. The stress−strain behavior of these (co-)polyesters largely depended on the content of BDM and covered a wide range from ductile to elastic to brittle materials. The films of these polyesters showed much faster hydrolysis under basic conditions, making them promising for future detailed degradation studies under different environmental conditions.