Submitting papers “out of logical order” due to different review times or rejections I am asking this question anonymously and apologize for the paranoia.
Suppose you submit a paper on a topic and, while the paper is under review, continue to work on the topic and make enough progress to prepare a second paper.  I know that submitting the second paper while the first is still under review is typical, but what do you do if the first paper is rejected around the time the second is submitted?  Similarly, what if the second paper is accepted and then the first paper is rejected?  Do you resubmit the first?
Note that the second paper doesn’t simply duplicate the results of the first in a more general setting; it relies on the results of the first and uses different techniques to extend them.
I know there are cases where the right thing to do (if the timing makes it possible) is to combine the papers into one.  But suppose this would be inappropriate, because the combined paper would be too long or too cluttered with different ideas.
So, specifically:

1. If the first paper is rejected right as you are getting ready to submit the second, do you consider it unethical or otherwise a bad idea to submit the two related papers around the same time (to different journals)?  This of course assumes the rejection was not based on issues with correctness of the paper.  Is it worth waiting a few months to submit the second paper to avoid an appearance of publishing “least publishable units?”  If not, should you explain it to the two editors with the submissions (more than just sending a copy of the first along with the second to help the referee)?
2. If the first paper is rejected AFTER the second is accepted, does the first just end up never being published?  Or is it ok to continue to submit the first paper, whose results have already been used and improved upon (though they are required in the improvement)?

 A: I really don't think this is a problem.
If there's a good / logical reason to combine the papers (and such a thing is possible by timing), that's fine.  But there might be many reasons why it's not appropriate - in addition to what you mentioned above, there might be two different sets of coauthors on the different papers, which can also make it tricky...
However, if paper #2 has already been submitted/accepted/published/is not easily combine-able, then I think you should resubmit #1 at your convenience, to whatever journal is most appropriate.  I wouldn't worry about paper #2 really at all in this decision.
In many subfields of mathematics, dissemination of results now happens largely on the arXiv.  Thus I think where / when the articles get published is becoming less and less important (although the prestige of an article in a good or top journal can still be useful for career reasons).
I've certainly been in situations like this and it hasn't seemed to be a problem.  I've also been a referee of papers in this position (both #1 and #2).  In the reports for papers #2, I usually note something like: "this paper builds on the work of paper #1 which appeared 3 years ago on the arXiv...."
A: The solution is preprints. Once you publish a preprint (through either arXiv or your own university server, although I recommend arXiv), you have a source to cite in the second paper and you can forget about the need of having it published before the other.
