Whenever I am working with buyers who have a strong interest in a property that goes under contract before they can make an offer, I encourage them to seek a backup contract IMMEDIATELY! You can follow this link http://db.tt/mw7ZbmEE
to see my blogpost, entitled The Anatomy of a Backup Contract.
The reason to act fast is that early in this phase of a transaction, the other buyer might start to ask for too much or otherwise not perform responsively and if the seller has your backup contract (signed and agreed, not sitting on the listing agent's desk), then there can be a strong motivation for the seller to deal firmly with the primary buyer and that may mean good things for you.
Of course, this is not the time to low-ball a property, but if you and your agent feel that at or above list price is prudent, then this is a low risk way to get a shot at what you want. There are a number of features to seeking a backup contract and perfecting your primary position that many listing agents may not be aware of. So, be sure to have a buyers' agent that knows the ropes.
Chuck Braxton, REALTOR