When Paul and Ieva Johnson moved from Minnesota to Florida, they were looking forward to warm weather and plenty of bargain-priced homes. But when the couple made their first offer earlier this year, they quickly discovered that they’d have to settle for the sunshine. Not only didn’t they get the house, says Paul, but “we didn’t even get a callback.” Over the next two months they put in seven offers — most at or above asking price — before finally making a successful $365,000 bid on a Sarasota three-bedroom. To their surprise, buyers in some housing markets are finding that they’re no longer in the power position. The reason is simple: too many bidders and not enough homes. A growing number of shoppers are on the hunt, confident that the market has hit bottom, say brokers. Yet many would-be sellers are staying on the sidelines, either because they’re underwater or because prices are still painfully low. Related: Best home deals in the Best Places to Live In June the number of houses listed for sale nationwide dropped 24% compared with the year prior, sending the supply of homes relative to buying activity down to levels not seen since 2006. That’s led to some stiff competition among buyers, says Sin-Yi Chao Lambertson, a broker in Glendora, Calif.: “I’ve had listings get 45 offers.” As the economy improves, the supply of homes should bounce back. If you’re in the market now, though, and want to ensure yours is the winning bid, take these steps: Size up your town. First you’ll need to determine whether you could be in for a bidding war. Rising price tags are a sign that sellers are gaining ground, but prices often lag the market. Related: Buy or rent? 10 major cities Two other stats, available on real estate site Zillow, can mean an area’s heating up: a drop in the percentage of homes with list price cuts, and an increasing ratio of sales to asking prices. Don’t skimp on credit. With many sellers worried about deals falling through, you’ll need the bank’s blessing right away. Don’t waste time on prequalification, which is an estimate of how much you might be able to borrow. “When multiple offers come in, I’ll toss out anything that’s just prequalified,” says Teri Herrera, a broker in Redmond, Wash. Pre-approval based on your credit, income, and assets is better, and full credit approval, which goes through the bank’s underwriting department, is best. Get a veteran on your side. Finding an experienced agent is even more important in a competitive market; you’ll want a pro who specializes in working with buyers and who knows the local players and pricing trends. “One of your first questions should be whether the agent has experience in multiple-offer situations,” says Herrera, adding that it’s also important to get details on the deals she’s closed recently. A good agent can help you determine whether a home is fairly priced, advise you on how much to offer — and back up her counsel with data and examples. Make a clean offer. When you take the leap, remember that “the best offer isn’t always the one with the best price,” says George Miller, the Johnsons’ Sarasota agent. “It’s the one with the fewest hassles and outs for the buyer.” Make yours as straightforward as possible. If it’s contingent on selling an existing home, for example, you’re unlikely to win a bidding war. Set on a certain closing date? Consider whether it’s worth blowing the deal. In this market, the answer is probably no.