“If you can do X, I will sign.”
…aying “can you improve the salary?” sounds like you’re boringly motivated by money. But if you say “I really want to buy a house within the next year; what can we do to improve the salary?” This suddenly seems a lot more legitimate.
It’s kind of a brain-hack, both for yourself and for your negotiating partner. Just stating a reason — any reason — makes your request feel human and important. It’s not you being greedy, it’s you trying to fulfill your goals.