Equivalents to Comptes Rendus The Comptes Rendus is (are) a French Academy of Sciences publication, essentially a 'rapid communication' format. It comes in many flavours, and maths is one of them. Proofs are non-existent (at least in older articles I've read), or perhaps only sketched. I don't know what the reach of CR is outside the francophone world (note that CR is bilingual French/English)
One preliminary question is this: 

Are there any equivalents to CR?

Some context: say I have a new result, which I know will be true, and just the grinding calculations need to be done. If I don't want to wait to unveil it to the world, what benefit do I get from publishing in rapid communication journals like CR? I could put the same thing on the arXiv, and while one might point out that a journal is refereed, but how can a proofless/proof-lite article be refereed?

Should I submit to a 'rapid communication' style journal while I finish the work, and then submit the full article elsewhere (+post on arXiv), or can I get away with a short arXiv note and then post and submit the full version when it is done?

 A: In the pre-Internet era, the role of CRAS was clear: publishing quickly announcements of results that would be published in full, later and elsewhere. To speed up publication, academicians or corresponding members had the power of accepting a note without having it refereed, with all the inherent risks (I remember the late Raoul Bott quipping, around 1983: "On the stock exchange, CRAS would be rated B"). Nowadays, in view of the role taken by ArXiV in quick dissemination of results, my feeling is that CRAS is more and more evolving to a journal publishing short papers with complete proofs, duly refereed, with the advantage of a quick decision process. In the committees where I've been recently, CRAS is rated as an ordinary journal. The only thing that would prevent me to submit to them, is Elsevier's pricing policy: see http://www.elsevier.com/wps/find/journaldescription.cws_home/621366/bibliographic
A: Electronic Research Announcements of the AMS is perhaps one such journal. But why not publish in Comptes Rendus? It is well known the world over and has many gems (with complete proofs). For example, Gabber's proof of a deep finiteness result in etale cohomology is in O. Gabber , Sur la torsion dans la cohomologie l-adique d'une variété. C. R. Acad. Sci. Paris 297 (1983), pp. 179–182.
A: I hope you will allow me to relate a cautionary tale.
Once upon a time, my co-author and I managed to find a counter-example to a conjecture, and we
wrote up a corresponding two page paper. We decided to submit our paper
to Comptes Rendus (the paper contained all the details, btw, given the existence of the ArXiv, publishing research announcements just seems like resume padding). I was in charge of handling the submission, and
so I naturally enough searched online for where to submit the paper.
My reaction upon finding the website was "oh, that's funny, Comptes Rendus
is a Canadian journal, I always thought it was a French journal".
Not thinking much beyond that, I submitted the file. Time went by, and, although I noticed that the journal seemed to be taking a long time to referee a two page paper, I did not think so much about it.
Six months later (to the day), the paper was accepted. I then noticed on the journal's website a note that said 
"On acceptance of a paper, to help defray the costs of
publication, a charge of 100 dollars will be requested." 
Somewhat nonplussed, I emailed the editor in chief whether this was true, and he confirmed indeed that it was, with the helpful remark that, and I quote,
"we assume that the researcher usually has a grant to cover such costs".
It was only at this point that my co-author realized my blunder. I was then in the awkard position of having to withdraw my paper from the Canadian journal
"Comptes Rendus Mathematiques" and submit it to the (French) journal
"Comptes Rendus Mathematique". This resulted in not only having to write one embarassing email but two: after asking to withdraw the paper the editor wrote me back and offered to waive the 100 dollar charge, thinking that this was the reason for my withdrawl.
In the end, it did get submitted to the correct journal, where it was accepted in two days.
A: While Electronic Research Announcements of the AMS mentioned in one of the answers are no longer there, they have a successor published by AIMS: 
Electronic Research Announcements in Mathematical Sciences (ERA-MS).
A: If you can, there's the Proceedings of the National Academy of Sciences. There's also the International Mathematican Research Notices, but this, I believe, is for short papers and not for just announcements.
