Joshua Bell is ubiquitous on New York’s concert stages. He seems to appear every other week. If it weren’t for the pianist Emanuel Ax, he could be champeen.

Luckily, Mr. Bell – a Hoosier violinist, as you know – plays well. He is one heavily publicized musician who actually deserves his celebrity. And he deserved his bravos in Carnegie Hall on Wednesday night, although he did not perform his best recital.

He certainly should have been applauded for the program he put together: an appetizing, well-balanced meal. He began with Mozart, moved to Beethoven, offered some Bartok, went to Prokofiev, and ended with his great violinistic predecessor, Eugene Ysaye. That is an “old-fashioned” program – but never out of style, as far as I’m concerned.

I might note that, over at Alice Tully Hall, the violinist Christian Tetzlaff and the pianist Lars Vogt played all three Brahms violin-and-piano sonatas. (This was at the same time as the Bell recital.) In the next few weeks, New York will have at least two more violin recitals, consisting of the three Brahms sonatas.

Come on, guys – that’s ridiculous. Brahms did not mean these sonatas to be presented bang, bang, bang. The completeness craze is absolutely nuts, and inartistic.

But back to Joshua Bell’s recital. He came out in his usual, open-collared black shirt, and was quickly up on his toes, swaying. That tends to be the Bell look, while he is playing.

The Mozart was that composer’s Sonata in G, K. 301 – and it was exquisite. Mr. Bell is an intelligent Mozartean: free but not loose; smooth but not soupy. Just a touch of flatness cast a shadow over this performance. (I’m referring to pitch.) Later in the recital, we’d have considerably more than a touch of flatness.

The pianist was Jeremy Denk, who did some excellent Mozart playing himself. (No pitch problems, on the piano!) He was solid – meaty – but sufficiently graceful. Some of his passagework positively rippled. And he gave the little peasant melody in the second movement a wonderful shape.

I should say, too, that this duo played some phrases together – strictly together – that aren’t at all easy to play together.

The entire sonata was characterful, alive, musical. Mozart’s violin sonatas can be nothingburgers, in the wrong hands. These were not those hands, thankfully.

The Beethoven on the program was maybe the mightiest of all sonatas: that in A major, Op. 47, nicknamed the “Kreutzer” (for its dedicatee, a French violinist). Our musicians were somewhat sloppy in this work, and not as convincing as they should have been.

The opening movement was fast, very fast – borderline rushed. Beethoven does mark it Presto, but you have to keep your wits about you. Mr. Denk missed notes, overpedaled, and messed with rhythm. Mr. Bell did not have his usual sure footing, and flatted like mad.

At the beginning of the second movement – the theme and variations – Mr. Denk committed some odd accents. Ungainly ones. Throughout this movement, he would play punchily, blockily, sometimes oafishly. A shot of elegance would have helped. Mr. Bell flatted some more, and rushed, and exhibited a rare superficiality. (He is not a superficial musician.)

The Finale is another Presto movement, and the two players duly took it like the wind. They were not unenjoyable. But this music does not have to be so rambunctious, so headlong. And Mr. Bell had a miserable time holding on to his pitch, in sustained notes.

This was not the worst “Kreutzer” you ever heard – in a sense, it was exciting. But the work seemed too big for Messrs. Bell and Denk, somewhat beyond them. I don’t mean technically, of course: Both of these guys have plenty of fingers. I mean mentally, spiritually. They simply failed to take the measure of the sonata.

After intermission, we had Bartok’s Rhapsody No. 1, and here Mr. Bell was in his element. He was flavorful, perceptive – finding just the right blend of spikiness and lyricism. Mr. Denk accompanied smartly.

Incidentally, I can’t be the only American – can I? – who, when the second part of this Rhapsody begins, thinks it’s going to be “Simple Gifts.”

Prokofiev wrote five wordless songs – vocalises – in 1920, and eight years later revised them for violin. That gives us the Five Melodies for Violin and Piano, Op. 35bis. Mr. Bell played – sang – sensitively, beautifully, allowing nothing maudlin, but allowing these small gems to unfold. This was a performance of the highest order, and Mr. Denk did his part, too.

Finally, the violinist let his hair down with Ysaye’s “Caprice d’apres l’Etude en forme de valse de Saint-Saens.” (Say that five times fast.) Here, the great virtuoso – Ysaye – was playing around with a study, “in the form of a waltz,” by his friend Camille Saint-Saens. In music like this, Mr. Bell seems born in a Viennese cafe, or a Parisian one, oozing charm and suavity. The piece is tremendously difficult, a test of a violinist’s technique – but Mr. Bell never seemed to be showing off. He was merely playing music.

Merely!

The one encore was a Tchaikovsky melody, which Mr. Bell rendered nicely, if with shaky intonation. You can’t have everything – although, at times in this recital, we pretty much did.