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Abstract To sum high-energy leading logarithms in a consistent way, one has to impose the strong ordering in both projectile rapidity and dense target rapidity simultaneously, which results in a kinematically improved Balitsky-Kovchegov (BK) equation. We find that beyond this strong ordering region, the important sub-leading double logarithms arise at high order due to the incomplete cancellation between real corrections and virtual corrections in a t-channel calculation. Based on this observation, we further argue that these double logarithms are the Sudakov type ones, and thus can be resummed into an exponential leading to a Sudakov suppressed BK equation.