Leverage disappears when desperation becomes visible.

Need is very difficult to hide. It shows in the speed of the reply, the willingness to move quickly, the questions not asked, and the terms accepted without discussion. Once the other side reads it, the terms change regardless of your arguments, because there is no reason for them to offer more. The position is lost before anything is said.

Where you can, build in time so you are not negotiating from urgency. Where you cannot, slow your own responses and finish the questions you would have asked anyway. Composure will not manufacture leverage, and visible panic will certainly remove it.