The second step for helping get your offer accepted is to not shop your maximum price range. Stay a bit lower so you have the ability to offer above listing price if needed. If you have a budget of 400,000 you should stay closer to 380,000. This gives you some wiggle room if you are in a multiple offer situation. In some lower 48 markets you may need even more wiggle room…ask your real estate agent how much the above list is typical so you know where you should be searching.
If you don’t have a great real estate agent, I’d be happy to recommend someone. I have connections to people all across North America.