Polymer flooding (PF) is an enhanced oil recovery technology that consists of the addition of polymer to the injected water to create a high-viscosity solution to control the mobility of the displacement process. Deploying polymers with high viscosity and maintaining high injection rate are two desired but competing attributes that impact the success of PF. In this research, we propose a simple, yet effective PF injection scheme that relies on the cyclical injection of compositionally-tuned slugs. This scheme achieves low polymer viscosity near the wellbore and high polymer viscosity away from the wellbore. This results in improved sweep efficiency compared to constant-composition injection, without impairing fluid injectivity. The new scheme harnesses known aspects of polymer rheology and rock interaction. We analyze the mechanisms that control slug mixing that include polymer rheology, inaccessible-pore-volume, and adsorption. Our results show that by injecting the compositionally-tuned polymer slugs with low injection viscosity, a higher polymer injectivity is preserved. Once the fluids mix in-situ away from the injector, the viscosity significantly increases, which improves sweep efficiency and incremental oil recovery over both waterflooding and continuous polymer injection. This new PF injection scheme can reduce chemical usage and improve the recovery effectiveness of PF, and therefore could be a potential alternative to conventional PF schemes.