Not to burst everyone's bubble, but JP, if it seriously is a really good story, TLE is the next-to-last class of place you want to send it (the last being Hadrosaur Tales). You want to hit the A-list markets first, like F&SF, Analog, Asimov's, and SCIFiction. Then the Bs like Aboriginal and Interzone. TLE is a C. A pretty-good-paying C, but its circulation is practically nonexistent, and that's no good.
If you know there is NO WAY IN HECK that the A or B publishers will take your manuscript, then send it to TLE first and hope they like it enough so it gets published and you can mention it in your cover letters for your NEXT story that you send to the As.
Now, of course, if you send it to the As, one at a time, it will be months and months, maybe a couple years, before you work all the way down to TLE. Gratification would be quite delayed. If indeed TLE did want it and the others did not. But if you sent it to TLE now, you'd hear back pretty darn quick due to it being shotgunned.