Eliminate repeat numbers from the last draw.
Here are some stats (figures are approx.)
575,000 combos minus numbers from last game leaves 278,000 combinations.
40% of the time there will be no repeats from last draw.
20 million combos minus numbers from last draw leaves 9.4 million combinations.
46% of the time there will be no repeats from last draw.
Mega Millions (white balls only)
3.9 million combinations minus numbers drawn in last game leaves 2.3 million combos.
68.5% of the time there will be no repeats from last game.
Conclusion: You can lower your odds by about 50% and be correct about 50% of the time by eliminating repeats in jackpot games.
[ EDIT ] Don't forget this lowers your odds of winning lower tier prizes as well.