One of the main challenges of the lattice design of e + e − synchrotrons, used as light sources or damping rings, is the minimization of the emittance. The optimal configurations for achieving the absolute minimum emittance are the theoretical minimum emittance (TME) cells. This paper elaborates the optimization strategy in order to further reduce the betatron emittance of a TME cell by using dipoles whose magnetic field varies longitudinally. Based on the analytical results, the magnet design for the fabrication of variable bend with the optimal characteristics is discussed. In order to have a global understanding of all cell properties, the analytical approach for the theoretical minimum emittance (TME) cells with variable bends is presented. Numerical examples for the linear optimization of the Compact Linear Collider (CLIC) damping rings (DRs) are shown. The margin provided by this new design strategy on the output beam parameters after including the dominant effect of intrabeam scattering, enables the removal of a number of TME cells from the existing arcs while still keeping the requirements of the collider. The reduction of the circumference is further enhanced by the use of optimized high-field wigglers. The optimization strategy followed for the CLIC DRs is explained in detail and the output parameters of the new design are presented.