The hybrid Diffusion-Transport Homogenization (DTH) method has been improved by replacing the assembly-level fixed-source calculation step with a fixed number of whole-core transport sweeps following each homogenization step. Like the unmodified DTH method, the Enhanced hybrid Diffusion-Transport Homogenization (EDTH) method adds an “auxiliary cross-section” term to the right side of the transport equation in order to maintain consistency with the heterogeneous equation. As an improvement to the DTH method, the on-the-fly rehomogenization step of the EDTH method utilizes a fixed number of full-core transport sweeps in lieu of assembly-level fixed-source heterogeneous transport calculations. The EDTH method has been tested in one-dimensional reactor core benchmark problems typical of a boiling water reactor core, a gas-cooled thermal reactor [High Temperature Test Reactor (HTTR)] core, and a pressurized water reactor core with mixed-oxide fuel. The method has been shown to reproduce the heterogeneous transport flux profile with 0 to 46 pcm eigenvalue error and 0.1% to 1.8% mean relative flux error with a speedup factor of 1.4 to 4.5 times faster than the DTH method. This represents a speedup of 3.0 to 12.5 times compared to fine-mesh transport.