What Sins said, except make it "until you can hire someelse or (date of your choice but definitely not ending before your notice would have,) whichever comes first.

Don't do what was recently done to me, however, unless you are willing to burn bridges with even the most understanding of bosses/companies. My only and essential administrative support staff just quit without proper notice. My company paid her "jack shit" for the work and skill level required, she was offered an unsolicited job at twice the money, but to take the job, she had to start immediately. She had to choose between conflicting values and commitments to her family, not to mention the need to pay the rent. She offered to work evenings for a couple of hours and on her one day off during the work week to do what she could to keep my little department afloat until I could find a replacement. My company has a policy that people who quit without proper notice are not eligible for rehire. It is very conceivable that at some point in the future she will want or need to return to my company - the largest employer in the area. I went to bat for her with HR regarding eligibility for rehire. 7 days later I arrive at work to find she had left her badge, key and brief note saying sorry, I can't keep working part-time, find some one else to do the billing that must be done by 5 o'clock that same day.    I'm pretty sure what happened, more or less sequentially, was she felt quite bad about leaving full-time with no notice, did not see she had a choice (she didn't, and we had talked about that) and then promised what she really wasn't willing to deliver in terms of working full time at the other job plus 12-15 hours per week in my department for another 4-6 weeks, and was too embarrassed and ashamed to at least tell me she couldn't do it. What happened was she offered those part time hours as a way to assuage her conscience, (with no pressure from me to do so, but with definite appreciation from me,) then couldn't deliver and rather than own up to that simply ran.

I personally wish her well and hope this new job works out for her and lasts. If it doesn't, however, she has made choices that have caused some doors to close and lock behind her.