squali83
The schools are tougher to get into because of the lack of available seats. However, if the adcom loves you, then you will be admitted.
I would add to Squali's point that a school that is lower in the rankings is bound to love you more than a higher-ranked school -- at least, I would think so. To illustrate with a hypothetical candidate:
This candidate scored a 700 on the GMAT - high, but not off the charts, especially when compared to top schools. Had a mediocre GPA from a solid but not prestigious state school. Has decent work experience for someone in his late 20s, but isn't the next Bill Gates, at least so far.
In other words, we've got a strong but fairly average candidate who won't stand out from the crowd at Harvard, but that lower-ranked schools would probably be excited to have.
But then EconGirl (both 1 and 2) had a good point - what about the yield game? Would Rice immediately scream "back-up back-up!" when they see your app, and assume it's a panic submission and ding your a$$ in an attempt to manage their yield rates? Does it matter if the reviewer is more likely to be cranky if she hasn't had breakfast, and she tends to get up later on Mondays and miss breakfast so you should try to time your app so that she gets it on Friday, which is statistically the most likely day for her to be in a good mood because she almost always eats breakfast on that day?
Agh. I guess my real point might be that all we can do is speculate on how the adcoms will really react. And if sending in more apps will assuage your rising anxiety as you wait for a reply from school #2, then go for it. (Assuming you really are willing to go to whichever schools you choose for the additional apps.)