This paper investigates the criterion for ultra-fast bubble walls in cosmological first-order phase transitions (FOPTs), focusing on the impact of hydrodynamic obstruction. The Bödeker-Moore thermal friction is typically used to determine whether a bubble wall can run away, but the friction on the wall is not necessarily a monotonous function of the wall velocity and could have a maximum before reaching the Bödeker-Moore limit. The authors compare the maximal hydrodynamic obstruction, a frictional force existing in local thermal equilibrium (LTE), with the Bödeker-Moore thermal friction. They find that for large parameter spaces, the maximal hydrodynamic obstruction is larger than the Bödeker-Moore thermal friction, indicating that the conventional criterion for the runaway behavior of the bubble wall may need to be modified. The authors also explain how to apply the modified criterion to particle physics models and discuss possible limitations of their analysis. They derive the critical phase transition strengths, α_n,crit^BM/LTE, above which the driving force cannot be balanced out by the maximal hydrodynamic obstruction or the Bödeker-Moore thermal friction. They define the ratio of the number of degrees of freedom (DoFs) in the broken and symmetric phases, b ≡ a_-/a_+, and find that hydrodynamic obstruction becomes more relevant than the Bödeker-Moore thermal friction in prohibiting runaway for b ≲ 0.85. The authors also provide a fit for the obtained α_n,crit^LTE(b) as a function of b. The paper is organized into sections discussing bubble wall dynamics, matching conditions, maximal LTE pressure in the detonation regime, maximal hydrodynamic obstruction, comparison with the Bödeker-Moore criterion, validity of approximations, and conclusions. The authors also provide a detailed analysis of the bag model and the μν-model, showing how the maximal hydrodynamic obstruction can be larger than the Bödeker-Moore thermal friction in certain parameter spaces. They conclude that the modified criterion for runaway walls in LTE is α_n > max{α_n,crit^LTE, α_n,crit^BM}.This paper investigates the criterion for ultra-fast bubble walls in cosmological first-order phase transitions (FOPTs), focusing on the impact of hydrodynamic obstruction. The Bödeker-Moore thermal friction is typically used to determine whether a bubble wall can run away, but the friction on the wall is not necessarily a monotonous function of the wall velocity and could have a maximum before reaching the Bödeker-Moore limit. The authors compare the maximal hydrodynamic obstruction, a frictional force existing in local thermal equilibrium (LTE), with the Bödeker-Moore thermal friction. They find that for large parameter spaces, the maximal hydrodynamic obstruction is larger than the Bödeker-Moore thermal friction, indicating that the conventional criterion for the runaway behavior of the bubble wall may need to be modified. The authors also explain how to apply the modified criterion to particle physics models and discuss possible limitations of their analysis. They derive the critical phase transition strengths, α_n,crit^BM/LTE, above which the driving force cannot be balanced out by the maximal hydrodynamic obstruction or the Bödeker-Moore thermal friction. They define the ratio of the number of degrees of freedom (DoFs) in the broken and symmetric phases, b ≡ a_-/a_+, and find that hydrodynamic obstruction becomes more relevant than the Bödeker-Moore thermal friction in prohibiting runaway for b ≲ 0.85. The authors also provide a fit for the obtained α_n,crit^LTE(b) as a function of b. The paper is organized into sections discussing bubble wall dynamics, matching conditions, maximal LTE pressure in the detonation regime, maximal hydrodynamic obstruction, comparison with the Bödeker-Moore criterion, validity of approximations, and conclusions. The authors also provide a detailed analysis of the bag model and the μν-model, showing how the maximal hydrodynamic obstruction can be larger than the Bödeker-Moore thermal friction in certain parameter spaces. They conclude that the modified criterion for runaway walls in LTE is α_n > max{α_n,crit^LTE, α_n,crit^BM}.