Since a W-4 is for wages, all of your wages will be reported to the IRS, so you can't prevent them from knowing. Your W-4 won't affect the amount you owe them, but only when you will owe it. You can overpay on each paycheck, and have them give you money back at the end of the year (if they have any money) by selecting 0 exemptions. Or you can underpay each paycheck and owe them at the end of the year by selecting many dependents or trying to claim EXEMPT, which may or may not be illegal.
Either way, they get their proper amount of money when you file your taxes at year's end.
The only way to decrease your taxes is to go after exemptions and deductions. But, unless the activities resulting in deductions were something you were going to do anyway (like buy a hybrid or install an efficient furnace in your home), then the deduction game is generally not helpful.
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