The orchestra of the Metropolitan Opera had a pretty busy weekend. On Saturday, they played Gluck’s “Orfeo” in the afternoon, and at night they played Puccini’s “Trittico.” That closed out the 2006–07 opera season. Then, on Sunday afternoon, they played a concert in Carnegie Hall, under their music director, James Levine. Where did they find time to practice? At Carnegie Hall, they did not sound underrehearsed.

Mr. Levine conducted two of his all-time favorite composers: Mozart and Carter. He also conducted Mendelssohn. How he feels about him, I’m not sure, but I can only imagine he is approving.

Elliott Carter (b. 1908) has been productive in the last five years. And the Met forces performed two of his works from this period: “Three Illusions” (I am counting that as one work, no snickering) and “Dialogues” for Piano and Chamber Orchestra.

Those “Illusions” have literary inspirations, and the following headings: “Micomicón,” “Fons Juventatis,” and “More’s Utopia.” The first piece bears many of the hallmarks of the modern age (an age you might also call Carterian). It is squirmy, menacing, bleak — filled with percussion. The second piece is scherzo-like, or at least mirthful. And the third is eerie, forbidding, ending violently.

Mr. Levine certainly knows his Carter — he is the composer’s foremost exponent — and he conducted the “Illusions” sure-handedly. Plus, the Met brass — I’m talking about hornists, trombonists, etc., not opera administrators — played very well. They were both rich-toned and agile.

“Dialogues,” as its name would suggest, is some kind of chat between the piano and the chamber orchestra. Carter fans must regard the piece as an example of masterly craft and inventiveness. Skeptics might consider it so much high-level doodling.

The piano soloist was Nicolas Hodges, a Briton described in his bio as “one of the most exciting performers of his generation.” And how did Mr. Excitement do? He played pithily and pointedly — somewhat excitingly, actually. Moreover, he turned his pages with aplomb.

As I often like to remind readers, Mr. Carter was born in the administration of Theodore Roosevelt, and next year we will celebrate the Carter centennial. That will be a major event on the musical calendar.

There were two big symphonies on this program, with Mendelssohn’s Third, known as the “Scottish,” on the first half. Mr. Levine conducted this work with wisdom and care. The restraint he exercised was for an evident purpose: to let the climactic moments have their due impact.

In the first movement, Mr. Levine took his time, but he was not ponderous. Often, the music had a layer of Scottish gloom — a desired layer, I should add. The second movement, in my opinion, should start on tiptoe. And it did not quite do that. I also believe that the playing should have been lighter: lighter both in tonal quality and in weight. Yet, this playing was far from bad, and the woodwinds were outstanding (as they had been in the first movement).

Mendelssohn’s Adagio was what it should be: songful, ominous, majestic, involving. The strings were stirringly dark, and the horns were superb. The last movement was just slightly sluggish, and it would have been lovely if the final chord had been together — but Mr. Levine provided satisfaction.

It would get better — a lot better. The program closed with Mozart’s Symphony No. 41 in C, the “Jupiter.” Now, critics like me have written about Mr. Levine’s Mozart many, many times: whether he is conducting operas, conducting symphonies, playing piano concertos, participating in chamber music. What is there left to say? I can say this: You can go many a moon without hearing a “Jupiter” so fine as Sunday afternoon’s.

It was crisp, alert, bouncy, vibrant, clear, precise, smart, and so very, very musical. Redundantly, Mr. Levine has proven himself the heir of the man under whom he apprenticed: George Szell. There was an all-time Mozartean; Mr. Levine is another.

I could register a complaint or two: For example, parts of the last movement were a little fast, cold, and unsavored. Additional regality would have been ideal. But one must not pick at this performance.

On occasion, Mr. Levine suffers from a lethargy. But in the “Jupiter” he was well-nigh wired. For one thing, he sang most of the way through — and did not sing softly, either. He seemed to be taken up. And speaking of up: In the final pages of the symphony, he stood. It had been a long while since I’d seen him do this: Mr. Levine has conducted sitting down for many years. So, it was startling to see him stand up. He looked like a giant, up on that podium. And he is one.