Negotiate like you mean it.
Working with clients, serious about buying in this market takes some negotiation. Find out as much about the property, the seller's motivation, and their closing date needs.
It's not always about the highest dollar amount. It may be the closing flexibility. Consider a substantial earnest money deposit, waving unnecessary inspections, and allowing some furniture to remain for a short period.
Some big pieces like a piano or pool table may need time for a pick-up, maybe allowing the seller to do a rent back.
Taking the property 'as is" with inspections and the right to withdraw may take the pressure off the owner. Consider waiving the radon, waiving the termite, waiving the appraisal, but only if you are confident about market value.
Make a cash offer even if you plan to take a mortgage or get a bridge loan, non-contingent on selling your home.
Have that back up financing in place. In this market, negotiating is not for amateurs.
Note: Make sure you can perform to avoid a legal suit. You want to protect that substantial deposit.
Find out what is most important to the seller.
In other words, negotiate just like you mean it.