A dream for sellers -- competitive bidding on their home -- is a buyer's nightmare. As a purchaser, how do you know how much to offer so you win a property without paying too much? What other factors besides offering more money can make you more attractive to a seller?

San Francisco residents Aimee Grove and her husband, Nate Wells, would like to know. The couple have been outbid on Bay Area homes twice since August, even though they made generous offers, have a good financial profile and wrote personal appeals to the sellers.

In August, they lost out on a $589,000 fixer-upper in San Rafael, Calif., even after offering $11,000 over the purchase price and a 20% down payment. The home had attracted four offers the first day it was shown, and their bid was the third highest, with the property selling for $615,000.

In a more recent multiple-bid sale, they failed to win a $599,0000 two-bedroom condominium in San Francisco's North Beach district that also needed work. The couple bid $650,000 with a 25% down payment and no contingencies -- the clauses allowing a buyer to back out of a sale for certain reasons. The owner asked for a higher offer, but the couple chose to stay put and be second in line if the winning buyer's contingencies caused the sale to fall through.

Ms. Grove eventually learned why they didn't get the condo. "I read in the homes-for-sale section in the newspaper that it went for $710,000," she says.

In the Northeast and Washington, D.C., regions, many parts of California and other desirable real-estate markets, competing against multiple buyers -- sometimes known as an overbid situation -- is a difficult fact of life. Learning what to offer is part science, part intuition, say Realtors. "With a market that's still extremely hot, it's the only way to be successful," says Linnette Edwards, an associate broker who specializes in San Francisco's East Bay area for ZipRealty Inc., an online real-estate company based in Emeryville, Calif.

She and other real-estate brokers offer these tips to help you fashion offers that outshine others on properties you want:

Be an informed buyer. Become knowledgeable about sales prices of homes in your desired area. Also know what you can afford to buy without overextending yourself and what lenders are prepared to give you. Remember, you'll need to reserve enough to pay other bills besides the mortgage after you purchase a property. For instance, in Manhattan, co-op boards want to see that buyers have enough money to pay the monthly co-op fees before they'll approve them, says Jane Goldberg, a vice president and associate broker at Century 21 Wm. B. May Co., a Manhattan real-estate firm.

Research recent sales prices on comparable homes. The asking price isn't always the best price to offer. A better gauge is the comparables, or "comps," or the recent final sales prices on similar homes near your target property. If other homes like the one you want sold for $50,000 over the asking price, "you want to bid to that highest dollar amount," says Stephanie Vitacco, a realtor with Coldwell Banker Residential Brokerage in California's San Fernando Valley, where sales prices average between $400,000 and $500,000. Real-estate agents should provide you with comps in your area, but they're also available on some Web sites, such as ZipRealty.com, says Ms. Edwards.

Research the sellers. Find out how motivated they are to sell and whether they want to buy another home. In this case, you might be able to make your bid more attractive by offering such concessions in your bid as allowing them to stay in your home for free -- also known as a "free rent-back" -- after the sale, Ms. Edwards says. Knowing whether a property is being sold to settle a will is also important, because these sales are mostly driven by how much money they can generate, she adds.

Factor in the number of other buyers making offers. The more bids being made, the higher the final price will go. Typically, competitive bidding raises prices by 5% to 20%, with 10 or more offers generating the highest amounts.

Write a letter to the seller. "Don't discount the emotional factor," says Ms. Edwards. One way to set yourself apart is to write what she calls a "love letter" to the seller describing yourself and your partner and children, if you have them, and why you want the house. You might even include pictures your children have drawn of the home.

Ms. Grove and Ms. Wells included a photo from their wedding and described themselves in a personal letter to the owner of the home they wanted in San Rafael. Although they didn't get the property, such letters often work because they set potential buyers apart and make the transaction less about money, says Ms. Edwards. "It sounds cheesy, but it does work," she says. "The cheesier the better."

One of her clients recently bought an Oakland Hills, Calif., home that attracted seven offers, even though the winning bid wasn't the highest. The two-bedroom, one bath home was priced at about $450,000. The seller was a single woman who had worked hard to restore the property. Ms. Edwards's client also was a single woman, so the Realtor advised her to write a letter describing herself and something she loved about the house and why she wanted it. Her bid, for about $500,000, was the second highest, but it was accepted.

Bid an odd-numbered amount. Most buyers typically offer a round number, such as $400,000 or $405,000 on a home selling for $395,000. Try to determine the highest amount you believe other bidders will offer. Then if you bid an uneven amount that's slightly higher, say $407,250, you may outbid the highest round-numbered offer and win the property, says Ms. Vitacco.

Recently, clients of hers bid against seven other buyers on a home near Los Angeles listed for $399,000. Their bid of $413,750 was successful, since the next highest offer was $412,000. "I didn't know where the next highest offer would go, but I did know that most people bid in round numbers," says Ms. Vitacco.

Make your offer as clean as possible. Try to remove every factor in your offer that might deter a seller. Include the highest cash escrow and down payments you can afford and as much as possible of the remaining payment in cash. If you need financing, secure a letter from your lender stating that you have been approved for the loan. Eliminate as many contingencies as possible; offer to have the property inspected quickly and to pay local closing costs, such as special taxes; and be ready to close as soon as possible. Don't ask for any appliances or fixtures that the owner wants and be sure to offer special assistance the owner might need, such as a free rent-back clause.

"Your ideal goal is for the seller to accept your offer outright, but they might counter you or make it a multiple-bidding situation, where the top three bidders can come back again," says Ms. Edwards. "If the seller likes the buyer, price, financing or narrow contingencies, those people will have a chance to come back to the plate."

Decide how much you really want the property. This is the critical issue in a multiple-bid situation. If you really want the home, you should make your strongest offer, because you may not have a chance to make a counteroffer later on, says Ms. Vitacco. "If the house meets all your criteria and this is where you are planning to stay, paying another $5,000 to $10,000 over 30 years is not going to change your life," she says.

When a home in the San Fernando Valley came on the market recently for $569,000, she knew it would fit one of her clients. He and four other buyers made offers, and Ms. Vitacco asked her client if he would be willing to make a higher bid. "He was willing to go the full price but no more," she says. "Psychologically, he couldn't do it."

Ms. Goldberg counsels buyers to offer as much as they can, as long as it's an amount that won't overextend them. "Then if you lose the bid, it isn't the end of the world," she says.

Formulate the final number yourself, with guidance from your broker. "You can't expect your broker to tell you what to bid," she says. "I try to lead buyers to a reasonable conclusion, but I hesitate to put numbers in other people's mouths."