Just before mortgage rates began their swift march upward, prices in 20 U.S. cities climbed 12% in April from a year earlier — the biggest gain since early 2006 when home values began to level off before the market collapsed, according to Standard & Poor’s Case-Shiller home price index released Tuesday. Some of the hardest-hit markets during the recession saw the biggest one-year jump, with prices in Atlanta, Detroit, and Las Vegas each rising about 20%. In Los Angeles, prices rose 19%, while prices in Boston, Chicago, and Denver increased almost 10%.

While we can breathe a sigh of relief at the double-digit increases, it likely won’t last. The rise in home prices is expected to slow later this year or next.

Don’t fret, though! This doesn’t signal the recovery has stalled; it’s actually a positive sign that the market is returning to normal.

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In the recovery’s next phase, home prices nationwide will rise slower by 8% in 2013 and even slower by 4% in 2014, according to Paul Diggle, property economist at Capital Economics. The firm’s outlook for next year is lower than the consensus of 5.5%.

The slowdown is a positive sign because if prices were to continue rising the way they have at 12% annually, homes would be overvalued relative to rents within the next few months and relative to incomes by early 2015, Diggle writes to clients.

Part of what was driving prices higher was demand from large investors, who bought foreclosed properties in bulk at deep discounts. Those properties have dwindled, however. And as prices continue to go up, investors aren’t seeing as many bargains as before.

As investors fade from the recovery, sellers are making a comeback.

It’s an important development, as many homeowners with mortgages worth more than the value of their homes resisted selling at a loss during the downturn. That has been changing, however. During the first three months this year, 850,000 homes returned to positive equity, according to CoreLogic. That means 19.7%, or 9.7 million, of all residential properties with mortgages were still underwater, down from 21.7%, or 10.5 million, the previous quarter.

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With home prices rising and fewer borrowers underwater, many more homeowners think it’s a good time to finally put up that “For Sale” sign, according to a May survey by mortgage finance company Fannie Mae. The share of respondents who say now is a good time to sell a home reached a record high of 40%, compared with 30% in April and 16% a year earlier.

The inventory of homes for sale bottomed in January and rose by 128,0000 homes, or 6.1%, since then, Diggle notes.

So if over the next several months prices aren’t rising as rapidly, know that the recovery is still strong; it has just entered another chapter.