What Should Wife Claim on W4 When Making Significantly Less?

My wife just picked up a part-time job making around $20/hr for 10-20 hours per week, and I need to help fill out her W-4.

This is significantly less than I make, and last 2 times she held a part-time job it created a tax problem for us at the end of the year. The first time, she marked married and her employer withheld 0 Federal and I had to pay $2k+ out of pocket at the end of the year.

The second time, she marked married and checked the multiple jobs box (as did I), but that just led to more taxes being taken out of my paycheck while she paid 0 federal. Doing this again is going to create some unnecessary financial stress with our tight budget.

This time, if she just checks single and 0 dependents is it going to be close enough to not cause a problem?