example for you, under US 121 regs: A VHHH to EGLL B744 flt plan ran straight, no redispatch, carried a 10% reserve fuel or 23,700lbs wiht a total fuel of 356400lbs. After doing the re-dispatch, 10% the reserve was cut down to 2200lbs and total fuel reduced to 329500lbs. That's just quick, and not altitude adjustments due to a lighter plane after doing the redispatch plane.
In this example, the flight was filed to EGLL, but the dispatch was to EKCH with a planned redispatch point at CHO NDB in Poland. Approaching CHO, the crew advises they have fuel required over CHO to continue to EGLL they get the re-dispatch. If not (or unable to contact dispatch or EGLL is now below mins or closed or whatever that might stop them from going), they go to EKCH.
As you can see, it's a pretty big drop in fuel required (and thus burned to carry the fuel). Our flight planning system will do an auto redispatch if we select it, but it's usually not as efficient as an actual person doing (either due to programming issues or the way we have it set up). In this case, the Auto Re-dispatch came up with a total fuel of 345100lbs