Submitting an improved result before the acceptance notice of another result I have submitted RESULT 1 to conference A. The notice of acceptance/rejection of conference A is in 1 month. This is the kind of conference with a rebuttal phase. During the rebuttal phase my paper got very good reviews, and all referees recommended acceptance. But that does not mean it is accepted yet. 

Some months after submitting RESULT 1, I obtained RESULT 2, which generalizes RESULT 1, but whose proof requires completely different techniques. I want to submit RESULT 2 to a conference B whose deadline is in two weeks.

I'm hesitating in submitting RESULT 2 to conference B before receiving the notice from conference A because of the following:


RESULT 1 gets accepted. Great!
RESULT 1 gets rejected. This is bad, not only because of the rejection, but also because since RESULT 2 implies RESULT 1, I think this would invalidade the possibility of submitting RESULT 1 to another conference 
while RESULT 2 is under review, or if RESULt 2 is accepted. I trully believe that RESULt 1 should be published independently, since the proofs therein are much more elegant, although not being the strongest result. 


My impression is that from the reviews RESULT 1 has a good chance of being accepted at conference A. However, I have had papers in the past with three recomendations to accept and which where rejected at the end. 

Additionally, I am afraid that by submitting RESULT 2 to conference B, my chances of being accepted at conference A would be decreased. For instance, a common referee could point out that a paper with a better result is being submitted to another conference before the acceptance notice, and this might influence in the decision of the programm commitee.

QUESTIONS: 


What is the best way to proceed in this kind of situation? 
Is it correct to think that submitting an improvement to conference B would decrease the probability of acceptance to Conference A?
Personally, when it comes to conference publications I don't worry about this type of issue.  

First, there is typically a fairly low chance that the second submission will affect the chances of the first: even in the unlikely chance that the same reviewer is looking at both papers at the same time, they are likely to understand that the second paper builds on the first: if they like the second, they'll probably suggest accepting the earlier result as well.

Second, and more importantly, conference publications are typically not the final form of a strong result.  Rather, the final form is the "extended version" journal paper that follows and supersedes the conference paper.
As such, if the second conference accepts while the first conference rejects, then there is still a clear path to publication for the results sent to the first conference: combining them together with the other results into a strong journal paper.  If the two results are related, the I think that you should be considering doing this in any case, given the typically larger scope of journal papers.

It is true that, in the worst case, it will give you one less conference publication for your C.V. If you're doing good research, though, that's not a big loss, since the work will be superseded by the journal paper in any case. Certainly it is less of a loss than not submitting to the second conference and getting rejected from the first (assuming both conferences are relatively similar in quality).