Spring homebuyers are pounding the pavement at a furious pace, but the pickings are getting ever slimmer.

Even as more homes come on the market for this traditionally popular sales season, they're flying off fast, with bidding wars par for the course. Home prices have now surpassed their last peak, and at the entry level, where demand is highest, sellers are firmly in the driver's seat.

"I've been selling real estate for 25 years and this is the strongest seller's market I have ever seen in my entire real estate career," said David Fogg, a real estate agent with Keller Williams in Burbank, California. "A lot of our sellers are optimistically pricing their homes in today's market, and I have to say in most cases we're getting the home sold anyway."

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Fogg listed a three-bedroom, two-bathroom, 1,240-square-foot home in Burbank for $789,000 and had three offers before the first open house Sunday. In the Los Angeles-area market, that is considered an entry-level home. The open house drew more than 100 potential buyers, most of them already weary of the competition.

"It's very tough. Most of the listings are intentionally listed a little low to get a lot of attention, and it's not uncommon to get 12 to 16 offers on one property," said Jilbert Mosessian, who has been renting in the neighborhood but wants to buy. "In three properties recently, we did our best, we went considerably over the listing price, and we were told that there were still five people above us and they were only going to deal with them."

More homes came on the market in March, but fierce demand made quick work of them. At the end of the month, the supply of homes for sale nationally was down 6.6 percent compared with a year ago, according to the National Association of Realtors. Unsold inventory is a slim 3.8-month supply. A balanced market between buyers and sellers has a five-to-six-month supply.

Properties sold in March were on the market for an average 34 days, down from 45 in February and 47 in March 2016.

In order to compete, buyers are coming in with cash and dropping contingencies. That is because in such a hot market, homes are appraising well below the sale price. That makes it even harder for first-time, mortgage-dependent buyers to succeed.

"I'm talking to the buyers in advance about these problems, so that we address the appraisal issues before we go to escrow and nobody is surprised in three weeks when we get an appraisal that's on the lower side," said Fogg.

As a result, home prices continue to hit new peaks each month. Prices nationally are up 5.7 percent in February year over year, according to Black Knight Financial Services. Washington, Oregon and Colorado are seeing the biggest price gains, as buyers flee high prices in California.

Real estate brokerage Redfin used its search engine to look specifically at which markets had the most people searching for homes outside their city. San Francisco, Los Angeles and New York took the top three spots. "Fast-growing coastal cities may be generating the high-paying jobs, but they haven't created enough budget-friendly housing to keep pace," said Nela Richardson, Redfin's chief economist. "The price of real estate and desire for homeownership is compelling many to uproot and seek housing in more affordable communities."