The semi-annual frenzy of art auctions begins this week with the sales of Impressionist and Modern art at Christie’s and Sotheby’s. Though the art on offer is elegant and meaningful, the most striking effect it produces comes from the prices. At both houses, the top dozen lots have estimates firmly in the eight-figure range.

That is fitting for an art market that is in the fourth year of a rapid acceleration. The boom that began in 1998 has had peaks and valleys. The year 2000 was a peak, according to Artnet, with nearly $3 billion worth of art sold at auction in more than 112,000 lots. From 2001 to 2003, the market struggled to return to that high point. But since 2004, the numbers have broken out. Last year, slightly more than $7 billion was spent on just shy of 150,000 lots. Total sales more than doubled while the number of lots only increased by about 34%. You don’t have to be a Wall Street wizard to see the price inflation there.

Those dollars aren’t chasing all the lots evenly. Demand for truly first-rate paintings is much stronger and deeper than for the rest. “There doesn’t seem to be a frenzy in the middle of the markets,” Sotheby’s head of Impressionist and Modern art, David Norman, said.

And some of the reason for that can be found in the behavior of the new collectors flooding into the market. They would rather own the very best work by a lesser-known artist — or the under-appreciated eras of a great artist’s work — than have a me-too picture. “New buyers are much more willing to make a record for a great, interesting painting,” Mr. Norman said. “It’s so quality-driven. It’s not hewing to decades-old rules.”

In the art market, quality begins with the painting and painter, then extends to condition and provenance. Christie’s has all of that in Matisse’s “L’Odalisque, Harmonie Bleue,” estimated at between $15 million and $20 million. In the same hands for 60 years, the painting has “a sensual line and vibrant palette,” according to Christie’s expert Guy Bennett. “A work of this caliber has not been seen in 20 years.”

Other highlights of the Christie’s sale include Paul Signac’s landscape “Cassis. Cap Canaille,” estimated at between $8 million and $12 million, which may capitalize on Christie’s spring sale of the artist’s harbor scene, “Arriere du Tub.” The sale also includes four canvases by Alexej von Jawlensky, but two Fauvist portraits—”Madchen mit Zopf,” estimated at between $3.8 and $4.5 million, and “Spanierin mit geschlossenen Augen,” estimated at between $3 and $4 million — are uncommonly good bait for the new collectors. And Max Beckmann’s “Stilleben mit Grammphon und Schwertlilien,” estimated at between $7 and $10 million, is a standout.

The irony is that these last three paintings in Christie’s sale run against the grain of the house’s emphasis. The Impressionist and Modern market is migrating. “For a number of seasons, the slant has been about the 20th century,” Mr. Bennett said, referring to the interest in Fauvism and German Expressionism, as well as other 20th century masters. “But one can’t discount the importance of the 19th century. The new collectors are bidding very aggressively for Impressionist pictures, which I feel are undervalued. I made a conscious decision to put a strong Impressionist collection together because that’s what our clients want.”

Indeed, Christie’s is selling a suite of four paintings by Pissarro, “Le Quartre Saison,” estimated at between $12 and $18 million, and a still life by Gauguin, estimated at between $10 and $15 million.

Sotheby’s sees the market going in the other direction — which makes sense and gives new buyers a competing, but complementary, vision. “We are much more focused on trying to win works by Feininger and Marc,” Sotheby’s Mr. Norman said of the German painters Lyonel Feininger and Franz Marc.

Despite the Gauguin on the cover of the catalog and their fair share of Sisleys and Cezannes, Sotheby’s is forging ahead under the banner of Lyonel Feininger’s “Die Grune Brucke,” estimated at between $12.5 million and $15 million, following last season’s world record $23 million for the painter’s “Jesuiten III.”

Franz Marc’s “Der Wasserfall,” estimated at between $20 million and $30 million, is an even bolder statement. Both works come from a significant moment in art history.

“We want these powerful visual statements because we think that’s where the market is headed,” Norman says. “We try to get everything, but we’re more aggressive on what we see the audience going after.”

Mr. Norman pays close attention to the bidding in his sales. He’s looking for the places where a group of bidders drops out, information that gives him a sense of where the broader market direction lies. “The constant evidence of the sales is that bolder outlines, simple forms, and strong blocks of color — real wall power — is what everyone wants.”

The preference for wall power filters back even to the French painters. Sotheby’s is selling Monet’s “Le Palais Dario,” estimated at between $8 and $12 million, which Mr. Norman describes as a painting “we really went for.”