An underrated tactic in sales is to explicitly say "I want you to have the best possible outcome here so I need to tell you..." and then give a short and honest recital of reasons to not do the deal.
Also works in recruiting, offering investment, etc. (The overwhelming case for me doing sales has been to folks who are deeply skeptical of sales professionals and believe themselves immune to salesmanship; this works *particularly* well in that context.)
If there are no reasons to not do the deal then *dig deep.* Even presenting your thinking process and degree of rigor can help your counterparty accurately perceive you as looking out for their best interests.
e.g. "You mentioned to me that the commute from the apartment is very important to you, and I thought we were probably not the closest apartment to the station, so I tried to map it out the four places you're looking at. I was actually surprised; turns out we are. Here's map."
n.b. I would not suggest doing this from a position of weakness in the negotiation; I'm thinking *particularly* of candidates here. There are some strong cultural norms to undercut one's own position there and, well, don't do that.
