Three-dimensional (3D) printing is becoming increasingly prevalent in tissue engineering, driving the demand for low-modulus, high-performance, biodegradable, and biocompatible polymers. Extrusion-based direct-write (EDW) 3D printing enables printing and customization of low-modulus materials, ranging from cell-free printing to cell-laden bioinks that closely resemble natural tissue. While EDW holds promise, the requirement for soft materials with excellent printability and shape fidelity postprinting remains unmet. The development of new synthetic materials for 3D printing applications has been relatively slow, and only a small polymer library is available for tissue engineering applications. Furthermore, most of these polymers require high temperature (FDM) or additives and solvents (DLP/SLA) to enable printability. In this study, we present low-modulus 3D printable polyester inks that enable low-temperature printing without the need for solvents or additives. To maintain shape fidelity, we incorporate physical and chemical cross-linkers. These 3D printable polyester inks contain pendant amide groups as the physical cross-linker and coumarin pendant groups as the photochemical cross-linker. Molecular dynamics simulations further confirm the presence of physical interactions between different pendants, including hydrogen bonding and hydrophobic interactions. The combination of the two types of cross-linkers enhances the zero-shear viscosity and hence provides good printability and shape fidelity.