This paper introduces a novel method for solving Schrödinger Bridges (SB) and Entropic Optimal Transport (EOT) problems, called LightSB-M. The method leverages the optimal parameterization of the diffusion process and allows for the recovery of the SB process in a single bridge matching step, regardless of the input transport plan. The key idea is to use the optimal projection of stochastic processes onto the set of SBs, which enables the recovery of the SB process without the need for iterative methods or heuristic approximations. The method is implemented using a Gaussian mixture parameterization of the adjusted Schrödinger potential, which allows for efficient computation and avoids the need for time-consuming MCMC techniques. The LightSB-M solver is evaluated on various tasks, including unpaired image translation, single-cell data analysis, and the SB benchmark. The results show that the solver achieves competitive performance compared to existing methods and converges quickly. The method is also shown to be closely related to energy-based modeling (EBM) objectives for learning EOT/SB. The paper also discusses the connections between the proposed method and other related works, including iterative proportional fitting (IPF) solvers, EOT solvers, and other SB solvers. The results demonstrate that the LightSB-M solver can recover the SB process using any reciprocal process, making it a versatile and efficient method for solving SB and EOT problems.This paper introduces a novel method for solving Schrödinger Bridges (SB) and Entropic Optimal Transport (EOT) problems, called LightSB-M. The method leverages the optimal parameterization of the diffusion process and allows for the recovery of the SB process in a single bridge matching step, regardless of the input transport plan. The key idea is to use the optimal projection of stochastic processes onto the set of SBs, which enables the recovery of the SB process without the need for iterative methods or heuristic approximations. The method is implemented using a Gaussian mixture parameterization of the adjusted Schrödinger potential, which allows for efficient computation and avoids the need for time-consuming MCMC techniques. The LightSB-M solver is evaluated on various tasks, including unpaired image translation, single-cell data analysis, and the SB benchmark. The results show that the solver achieves competitive performance compared to existing methods and converges quickly. The method is also shown to be closely related to energy-based modeling (EBM) objectives for learning EOT/SB. The paper also discusses the connections between the proposed method and other related works, including iterative proportional fitting (IPF) solvers, EOT solvers, and other SB solvers. The results demonstrate that the LightSB-M solver can recover the SB process using any reciprocal process, making it a versatile and efficient method for solving SB and EOT problems.