Is there anyway I can avoid owing?

Are you sure you are doing Single with zero and not Married with zero. Something doesn't sound right here, the way the tables are constructed is for your situation exactly. If you are claiming single and you still owe, the payroll department may not be reading the tables correctly or the computer is setup incorrectly. Therefore, you have two possibilities, point it out to the payroll department and have them correct it or on the W-4, have an additional amount withheld out of each pay period. Sidenote: do you have other sources of income (i.e. interest, dividends, self employed income) that isn't being taxed?