Abstract: A labyrinth seal system for reducing leakage flow of a compressible fluid between a rotating portion of a machine rotating relative to a stationary portion of the machine. A stator seal element is connected to the stationary portion of the machine and a rotor seal element is connected to the rotating portion of the machine. The rotor seal element defines a plurality of staggered cavities. Straight long teeth connected to the stator seal element define throttling clearances with the bottom walls of the staggered cavities of the rotor seal element, and short teeth connected to the stator seal element slanted upstream relative to the direction of leakage flow define throttling clearances with the rotor seal element. Undercuts can optionally be defined by the rotor seal element on the downstream side of the cavities. Optional straight teeth connected to the rotor seal element downstream of the cavities define throttling clearances with the stator seal element.