Tenured Radical is also in the academic advice business, and has a wonderful post on applying for a job when you already have one. I started writing a comment and it got so long, I thought I’d just post it here.
WHY NOT TO USE LETTERHEAD. I actually don’t think people should use their current institution’s letterhead when applying for a new job (most of the time). You are, after all, selling yourself and trying to separate yourself from the institution where you work. The letterhead is a reminder for the committee of where you’re at and doesn’t necessarily confer any advantage: either you’re at a “good” place (please note ironic scarequotes) and they wonder if you’re really serious about leaving (or why you are) or you’re at a “bad” place and therefore get no points for being there. Also, you’re applying as a person, not a functionary of the institution (as opposed to using the same letterhead for a recommendation). Basically, I think it’s the “don’t use letterhead for personal business” rule; don’t do it for the same reason you don’t dispute suspicious charges to your credit card on letterhead.
THE STORY OF WHY YOU WANT TO MOVE: I think the #1 rule is simply to speak in positive terms — why you are excited about the new opportunity and place and what you hope to accomplish there. The less you say about where you are (beyond the standard “I am currently an assistant professor at such and such a school”, generally speaking, the better.
IS IT UNETHICAL TO APPLY FOR ANOTHER JOB WHEN YOU HAVE ONE? No, never, unless you are actively deceiving someone about something. No matter how much capital people spent to get you to a place, it is a market, you are absolutely entitled to test it any time you want and for any reason. Of course, you can’t keep approaching your institution for counteroffers, and I don’t recommend going on the market frivolously (if you’re not serious about it, there is really no point and a lot of damage to be done) but those are other issues. Colleagues may be mad that you applied for another job, but they are either naive or they resent that you have the possibility to move (either because of your life situation or the quality of your work).
NEGOTIATING LEAVES AND TENURE CLOCKS: These issues totally depend on a) the school and b) how badly they want you. In a unionized environment there may be strict rules about progress toward tenure. McGill’s nonunionized environment also offers no flexibility on sabbaticals, for instance. Elsewhere, it may be up for grabs and a lot depends on the attitude of the chair and the dean. My attitude is always that once a person is a legitimate candidate for tenure, it’s wise to tenure the person. Of course the downside of early tenure for the candidate is the increased service expectation post-tenure.