How to tell a company offering me a job to wait a little?

"ASAP" is almost always just a management technique. Of course they want an answer right away, but that's no reason to submit to a hustle. You want the best job and offer possible, so asking them to wait a week shouldn't be a foul. Disclaimer: I currently have a job.

ASAP answers make sense for company A as recruiting is a massive pain in the arse and the sooner they close the deal the better it is for them. You could accept the offer to later decide to reneg ... that is the idea of the probationary period ... and it is a common occurrence ... but it ain't professional IMHO. Option 2 is stalling ... ask for more money and better conditions, tell them that your laywer will need to review the contract, send them back a marked up version of the contract for them to review, send their version of the contract back to your lawyer for a 2nd review ... that has to be good for a week and a half of stalling. Ask them to explain their understanding of the [non-compete clause] [confidentiality clause] [some other clause in the contract] with reference to [your industry?] ... tell company B that you have another offer pending and they need to make up their minds ASAP ... even to the point of moving your interview forward to expedite the process.

I would tell them you are considering all offers, just like if you were selling a house, and you need another week. They may up their offer!

Oh: if Company B had not gotten back to me two days later, I would have first called Company B to try to get a response. Without a response from Company B in time for the 1 week extension I got from Company A, I would have taken the job with Company A.

I was in this exact position a couple months ago. My industry is very tight-knit, and people talk. I asked Company A for an extra week to make my decision. They said OK. I think they realised I wanted to work at another company, because they called me the next day with a slightly better offer. At my interview with Company B, I (quite honestly) explained that I needed their offer within two days, so I could take care of other employment offers. I presented this like I wanted to "be fair" to other companies, and I implied that it was inflexible. Company B offered me the job two hours after our interview :) Remember, they want you to work for them. They might not like it, but they're unlikely to give up on your offer just because you need an extra week.

I'll concur with previous posters. I've seen people start a job and quit a few weeks later for something better. People are miffed, but a month down the road, everyone has forgotten their name. It's not a huge deal (depending on your line of work - perhaps this would not work well for lawyers. It works for DBAs.) And, as others have said, tell them you need another week or two. They'll probably give it to you.

Do you work in any kind of niche industry at all? Or one where reputation or networking is important? Or even just somewhere geographically somewhat small? Because being anything less than straight with these companies is going to look bad, and taking then dumping a job most definitely will piss them off and word will get around too. This can hurt your future career including with company B, I've seen it happen. Think carefully about implications before you make this kind of move, I've seen the resulting reputation follow someone around for years. I work within a community ('the research science community') where this shit matters, you may not. Tell them you need an extra week. Tell them you have other options to pursue. Give them a deadline by which you can make a decision so they're not left hanging. Then negotiate from there. Most companies will understand and give you some leeway. At the least they'll tell you why they need to know so soon and you can decide how to deal with that. Don't lie, don't dick them around, act with integrity, then suck it up and make a decision.

My default answer, when anyone wants a decision now now now is always "No." I seriously doubt they need you that darned soon. Typically, people pressure you for an answer in order to deprive you of the ability to think things through. They want you to say "yes" because they are afraid that, if you had the time to look over the data, you'd say "no." Alternatively, there's some Type A guy in the food chain who bangs around a lot and has to have everything instantly, including new job hires. Boy, that sounds fun to work for. Neither is an appealing cause for their sudden demands.

Unless Company A and B have a special relationship where they hug each other all day and share things, than you accept with Company A, and put the start date (you need to move right? right?) a couple weeks ahead. You wait for Company B. I've accepted and then recanted the next day. It is not a big deal, unless you are a c-level position.