I think it's a tricky situation but not a moral one until you lie to either firm, which I don't think you need to. As the post from Ayvik states, its quick likely that either firm would not give the same consideration that you're already giving them.There have been 2/3 very similar posts that I would encourage you to search for (at a quick glance I can only find one 32110 with a reply from Tony). You mention that you've received 'an offer to come for an interview at one of the "higher" companies'. Obviously, this may not materialise into 'a job offer' so if you've already handed in your notice to your present company it could be a real gamble turning down the offer you already have and pursuing an interview process with the one you really want. Having said that, if you really want job number 2 then maybe you should just go for it. The only advice I would give you is to not lie to your present job offer (which doesn't necessarily mean explaining the whole situation), and possibly somehow speeding up the interview process with job number 2. If you turn down the already signed contract (see the thread above regarding implications), then be professional about it and avoid burning too many bridges (which you never know when they come back in handy!)Hope that helps!