The world is groaning with mezzos, among them Olga Borodina, Anne Sofie von Otter, and Vesselina Kasarova. And Susan Graham, Susanne Mentzer, and Stephanie Blythe. I could list on and on. Complain about conductors if you want to, and certainly complain about composers — but don’t complain about mezzos.

One of our outstanding mezzos is Magdalena Kozena, who gave a recital in Alice Tully Hall on Sunday afternoon. In recent years, she has been a glamorous opera star — almost a celebrity, really. But, years ago — when she was less famous and less glam — she made one of the best Bach compilations known to me. (It’s available from the Archiv label.) So this is a formidable musician.

At Alice Tully, she sang a wonderfully mixed program: a set of lieder, a great song-cycle (also in German), a French set, and a group in her native tongue — Czech. This mixture was most welcome, especially if you, like me, are sick of one-composer recitals (and one-themed recitals).

She began with five songs of Mendelssohn, the first of which was “Pagenlied,” a simple thing, sung simply. Ms. Kozena has an enviable musical awareness, and she knows how to communicate. But, in “Pagenlied,” she sharped a bit — just a bit — as she would continue to do for much of the evening. And the voice seemed thin — almost as thin as this opera star herself has become. It lacked the body and resonance it has customarily had.

If you’ll allow me a concern: More than a few singers have ruined themselves by getting Hollywood thin. I trust Ms. Kozena bears this history in mind.

“Venetianisches Gondellied”is a sad barcarolle, and she sang it well, but other Mendelssohn songs went less well: “Nachtlied” lacked richness, lushness. And “Neue Liebe” was far too heavy. It is practically a Mendelssohnian scherzo. And you know who sang it really, really well? A singer it is fashionable to despise: Kathleen Battle. I doubt anyone has ever sung it better.

After her Mendelssohn, Ms. Kozena sang Schumann’s “Frauenliebe und – leben,” sacred province of mezzos. If you were present for a Kathleen Ferrier or a Janet Baker performance — or a Christa Ludwig performance — you were lucky indeed.

Ms. Kozena sang some of the slower songs rather too slowly — almost dully — and she had this problem elsewhere on the program, too. More seriously, there was that thinness, or insubstantiality, of sound. Ms. Kozena seemed to be in some (vocal) distress. I thought of an old chestnut: “Sing on your interest, not your capital.” Is Ms. Kozena bearing down on her capital?

“Er, der Herrlichste von allen” — that incredibly stirring song — lacked guts, and heft. “Du Ring an meinem Finger,” similarly, needed more plumpness. And “An meinem Herzen, an meiner Brust”didn’t have the ecstasy it ought to have.

But Ms. Kozena, as I’ve said, is no dummy, and she took us on Schumann’s journey. What an eternally great song-cycle.

After intermission, Ms. Kozena offered seven songs of Fauré, beginning with “Le papillon et la fleur.” I’m afraid it was missing its key ingredient: charm. “La rose” was good, treated with uncommon nobility. But “Mandoline,” like Mendelssohn’s “Neue Liebe,”was much too heavy. It also deserved a steadier tempo. And Ms. Kozena failed to take the pleasure in this song that a singer ought to take — that, despite one, nicely saucy portamento.

The aforementioned Dame Janet (Baker) used to kill you with “Rêve d’amour.” It was so direct, honest, and unadorned, you could hardly bear it. Ms. Kozena exhibited some of these same qualities. But “En sourdine,” unfortunately, requires more purity of sound than Ms. Kozena was able to give on Sunday afternoon.

She ended her printed program with Dvorak’s “Gypsy Songs,” which used to be sung in German, before singers — most of them — got wise to Czech. Ms. Kozena sang these songs ably, as she could not help doing. But I must say I have seldom been so unmoved by this set. I would point out, too, that nationality isn’t everything in music-making — even in singing (where it probably counts most).

For her encores, Ms. Kozena continued in her native repertoire, singing three songs, and doing so with as much authority and style as she displayed all afternoon.

In the time-honored tradition, I will devote my final words to the accompanist. (Gerald Moore used to say that his mother was the only person who read reviews from the bottom up.) He was Malcolm Martineau, one of the best in the business, prized by singers all over. He did his usual admirable job. In Mendelssohn’s “Hexenlied,” he showed a fair amount of technique, and elsewhere he demonstrated fine soft playing. Also, he imitated some of Ms. Kozena’s cutesy rubatos, as a good accompanist might.

A couple of reservations, however: Mr. Martineau could have been far smoother in Fauré’s “Spleen.” And since when has he indulged in hammy expressions — meaning, facial expressions — directed at the audience? I had seen and heard him a hundred times before, and never noticed that.