NEW YORK ( TheStreet) -- Little by little, we're starting to hear reports of bidding wars on homes. It's hardly a flood, but it provides yet another sign the housing market is getting stronger. A tug of war over a home may come as quite a surprise for anyone who assumes it's a buyer's market. The key factors: Mortgage rates remain low, giving buyers more money to spend; prices are rising, making buyers feel it's worth the risk to pay full price; and the number of homes on the market remains fairly low, raising the odds there will be more than one buyer for a given home. So how do you handle your offer if you're concerned about rival bidders? Start by keeping in mind the two key factors every seller puts first and foremost: Sellers want top dollar; and they want to be confident the offer they accept will make it through the process to closing. The last thing the seller wants is to accept a generous bid, then miss out on other buyers while waiting a month of two for a closing that doesn't take place because the buyer can't get a loan or pulls out for some other reason. HSH Associates, a mortgage data firm, suggests the buyer reassure the seller by getting a mortgage pre-approval. Stronger than a pre-qualification, a pre-approval means the lender has checked your financial health and found you worthy of getting a loan of a given size. It's not a guarantee you'll get the loan, but it shows the buyer your risk of denial is pretty low. Given two offers at the same price, the seller is likely to favor the buyer with the pre-approval over one who doesn't have one. You can enhance your chances of being pre-approved by correcting errors in your credit history, paying down debts and getting rid of unneeded lines of credit. Of course, your bid would be even stronger if you did not have to make it contingent on getting a mortgage or selling your current home. But if, like most buyers, you must have a mortgage contingency, don't set a maximum loan rate so low it's nearly impossible to get. That would be a red flag, looking as if you're leaving yourself a way out of the deal. A second strategy, according to HSH: Make your best offer first. If you think a bidding war is likely -- something your real estate agent should investigate -- don't make a lowball offer just to test the waters. A rival may bid enough to get a deal before you have a chance to raise your offer. Figure the maximum you're willing to pay and offer that or something close. Next, don't be too demanding on marginal issues such as requiring that the washer and dryer come with the home. Some buyers hold firm on minor issues out of pride, to show who's toughest. But it wouldn't pay to lose out on your dream home over an appliance that's on its last legs anyway. Finally, have your agent probe to find out if the sellers have any concerns of especially high priority. If the sellers, for instance, wanted some flexibility on a moving date, you could offer to let them stay on for a short period at a minimal rent. Or, if the seller is eager to get out, you could offer to close earlier than scheduled if your loan comes through. Even a minor issue, such as being flexible on the time and place for the closing, could tip the balance in your favor by making you seem easy to deal with. Dickering endlessly over trivial matters could push the seller into another buyer's arms.