As Surveyor mentioned, look to your employer(s) to take advantage of possible tax-savings vehicles. The 401(k) is the best idea as you can reduce your taxable income quite significantly (today) without having to change your withholdings to zero. Also, if they offer a flexible spending account for health care, you can contribute to that. Just make sure that you don’t contribute more than you’ll actually spend on health care, because it’s “use it or lose it.”
Also, as someone mentioned (I don’t remember who it was), make sure that when you do the comparison between what you would owe without the other spouse’s salary, you’re switching the filing status from married filing joint to married filing separately (which in my opinion is the worst filing status) so that you’re comparing apples to apples.
If your company doesn’t have a 401(k), you can consider contributing to a Traditional IRA to decrease your tax liability. The limit that you can contribute is lower than what you can in a 401(k) [401k is $15,500, IRA may be $4k or $5k??], but it can help too.