Time for Three offers arrangements of music by everyone from Katy Perry to Leonard Cohen to Bach. (Sherry Ferrante)

The musicians of the trio Time for Three have been playing together since they were students at Philadelphia’s Curtis Institute of Music some 14 years ago. Curtis is both a conservatory and a buzzword — it is known for taking the best music students in the world.

The name is a bit of a crutch for the trio, which purports to be a genre-busting ensemble, offering engaging, energetic arrangements of music by everyone from Katy Perry to Leonard Cohen to Bach with a kind of bluegrassy-pop-fun-times vibe. But the stylistic mishmash is never quite natural; it remains a departure, because the players are Curtis-trained.

It’s great to see crack classical players horsing around and having fun, but the classical training remains their default mode, the place where they really shine. If they weren’t classically trained, their eager, not-quite-polished shtick would fall flat, and audiences might not be as tolerant of their stylistic explorations — which, frankly, aren’t quite as good as their classical playing.

Time for Three, or Zachary De Pue, Nick Kendall and Ranaan Meyer, came to the Fortas Chamber Music series Monday at the Kennedy Center, and throughout the evening, the musicians expressed their deep gratitude for being there. They are hardly strangers to mainstream concert halls; Kendall, in fact, is featured this season in many of the National Symphony Orchestra’s youth concerts, and De Pue, the other violinist, is concertmaster of the Indianapolis Symphony Orchestra. Meyer, the bassist, has a jazz ensemble and a composing career, and the trio performed several of his original pieces Monday — a running gag through the evening concerned the titling of his works. (One piece was called “Don Don,” named for the sound that a bass makes descending the strings; “that was before the guys took away my right to name our pieces,” he quipped.)

The group is trying to forge an alternate pathway for itself, establish a distinctive musical identity outside the classical music norm and, perhaps, make some money. From self-producing CDs when it started out, the ensemble has moved up the food chain of record labels (its first recording for Universal will come out later this year). But one reason that it remains so endearing — and it’s hard not to like this group — is that it doesn’t quite succeed at the level of glossy entertainment. The players — and the act — are not quite as polished as they could be. That is at once a handicap and a virtue. The group is trying to be cool, but it isn’t really as cool as it wants to be.. Therein lies its charm.

The performance allowed plenty of room for meditation on classical convention and popular stylistic variants, starting with a tuning session that wanted to blossom into an actual improvised number but didn’t fully launch. Classical training traditionally focuses on clean, beautiful production, while popular styles sometimes place more of a premium on expression. The result, when classical players cross over, is a kind of deliberately muddy or hoarse tone — think of it as the Bob Dylan effect.

That came out in an arrangement of Leonard Cohen’s “Hallelujah,” which was paired with Imogen Heap’s “Hide and Seek” on the slow part of the program. The most striking moments, though, tended to be the fillips and snatches of singing tone, especially from De Pue, and the most effective slow song was an arrangement of a well-known Bach chaconne, presented in a mash-up with a song by the group Bon Iver.

It was certainly a pleasant evening, even if it dragged a bit in places. And it concluded with the piece that has remained this group’s ace in the hole for most, if not all, of its existence: an arrangement of the “Orange Blossom Special” laced with fingerwork and whoops and hollers, played about as fast as human fingers can probably take it.

Since there was nowhere to go but down, the group offered a mellow “Amazing Grace” as a relaxing encore to send its listeners out into the night.