I am sorry, but exception made to #2, I respectfully disagree with ALL the other suggestions here.
1. Don'i limit your availability, MANAGE it!
Learn to make 100% reliable turnaround time estimates. This involves knowing your production level and capabilitiy, but it's not rocket science. I never missed a translation deadline in four decades, so I was quite young when I began doing it.
Every time a prospect approaches you with a request, check your current workload, and tell them when you can certainly deliver it. If they want it earlier, don't take it up blindly. At best, you can tell them something like "I can promise that I'll deliver it by Friday next week. This means that I'll strive to have it finished by Wednesday or earlier, if I can. However I won't promise it for earlier than Friday."
3. Don't use the competition, they may use it against you too.
Keeping it short, this is a real case... A client called me to say that my proposed price for a big job was too high; they had found someone 25% cheaper. I thanked them for the heads up, so I wouldn't stay awake waiting for their order. They said, "No, we want YOU to do it for 25% less!" I told them that it would be blatantly dishonest if I lowered my price onlly because they had found someone cheaper. My first estimate would have been an attempt to rip them off. That is my price, and I know it's worth every penny. On the other hand, I have no idea on what the cheaper vendor will provide them.
Epilogue: I got the order at my price. Also, I'll never know if they really had someone 25% cheaper, or not.
Lesson: If you know your price is right, stick to it.
4. Biased choices often lead to a waste of time. The prospect will try to flex one or another of these options, so you'll be back to square one.
The best solution is to tell the client the best you CAN do. If that's not enough for them, they should seek someone else. Chances are that if what they want is impossible, they won't find anybody.
Keep in mind that the client is NOT at all interested in what you CANNOT do. Thell them what you CAN do.
5. Don't negotiate on fees. In any trade other than translation, the seller is the one who sets the price. Make sure your price is right, and stick to it.
However this should be your "prime time" rate. You may negotiate your otherwise idle time (e.g. between projects, when someone else is reviewing your work, etc.). If the prospect is hard for cash, but in no particular rush, in exchange for a longer turnaround you may lower your rates. (As a benchmark, if the deadline is changed from X weeks to X months, I lower my rates by 30%. That's how I translated several books.)
This will spare you from taking a job at a low rate, and (pursuant to Murphy's Law) immediately afterwards being offered a higher paying assignment, which you can't accept, because your prime time is already taken.