As a Buyer: How do you deal with competing offers?

This post refers to standard 'homeowner to homeowner deals, not (REO) bank owned properties--they will more often than not say there are multiple offers when there are none.
You have found the perfect home, crunched the numbers and decided make an offer. But---when your agent submits the offer, you find out that there are multiple offers. At this point, you are told by your agent that the listing agent has told you to submit your highest a best offer.
First things first, you need to take all things into consideration and decide how much you are willing to pay for that home, regardless of how many offers are on the table. It is important not to get caught up in the competition aspect of producing the 'best offer'. Once you have made a decision about how much you are willing to pay for the home, submit that offer and be ready to deal with what happens. Do you’re very best to remove all emotion from your offer. This is a business deal. Treat it as such. You may not get the home because someone else might be willing to pay more for it, but if you get into the bidding war then you will pay more that you normally would have--and it may be more than you can really afford.
On top of increasing the home price, you might also want to consider other options in your offer, including a shorter or longer period before the closing date, paying more in closing costs or taking some issues such as dirty carpets as is. A motivated and agreeable buyer may have better luck than a picky buyer with a higher offer. Many times, getting rid of the hassle is as valuable as the higher price.
Good luck with your home search and remember the next time you hear someone talking about how they would like to sell their home I would really appreciate an introduction. My email is mike@teamtobin.com