Something old, something new, something spiritual, something internal: Miami-born artistic director Robert Battle’s quest to push the Alvin Ailey American Dance Theater in new directions while holding tight to its roots was evident as America’s most famous modern dance troupe opened its Adrienne Arsht Center run Thursday night with four disparate works.

The opening Petite Mort by European contemporary ballet choreographer Jiri Kylian represented the biggest departure from the company’s full-tilt physicality and full-bodied movement. Highly stylized, visually witty and ironic, the piece is not done in toe shoes, but it demands prodigious technique, precision and clarity, which the Ailey dancers managed admirably. (Interestingly, they seemed more comfortable with the ballet than with the buoyant, athletic precision of Paul Taylor’s Arden Court, a major Battle addition last year.)

Petite mort, (“little death” in French) is, of course, a euphemism for orgasm, but Kylian cloaks the sex in fiercely elegant partnering and clever visual puns. Corset-like trunks and tops and Mozart piano concertos provide an ironic 18th century atmosphere.

The dance begins with the six men swinging rapiers (a phallic emblem?) in sweeping formal patterns, and then the six women maneuvering behind elaborate ball gowns with hidden wheels. A series of intense duets often end with the men balancing horizontally, arms outspread, on top of the women. Linda Celeste and Glenn Allen Sims’ symbiotic connection and Jamar Roberts and Alicia Graf Mack’s long lines and sensual grace were particularly striking. Petite Mort isn’t deep, but it’s terrifically and smartly entertaining.

Grace, which Ronald K. Brown made for Ailey in 1999, is an audience favorite that beautifully suits the company’s talents, and it’s good to see the complete piece again in Miami. Commanding Linda Celeste Sims leads 10 dancers in a spiritual voyage that is both celebratory and ritualistic, the dancers moving fluidly between flying-limbed African, hip-hop tinged club and open-armed devotional dance as the music segues from a Duke Ellington spiritual to electronic dance, Fela’s pulsing Afro-beat and back to church. The dancers keep opening their arms and chests to light beaming down from on high, sometimes confrontational, sometimes questioning, finally accepting. Matthew Rushing’s gravity, Demetia Hopkins’ fiery force and Rachael Mclaren’s electric energy stand out. Dancing is a sacrament in Grace, whether in church, club or village circle.

The statuesque Roberts, another Miami native, seems a counterintuitive choice for Battle’s frenzied, contorted solo In/Side, but he turned out to be an interesting one. His innate smoothness is startling in the jittering, jagged movements, and his physical power strengthens In/Side’s agonized internal battle as he arches on the floor in a silent scream. Robert’s commitment made this intense but emotionally constricted dance mesmerizing, and the audience roared its approval.

Revelations has become a kind of Miami ritual, and on Thursday the company performed it with familiar but still satisfying precision and enthusiasm. The yearning Fix Me, Jesus duet by the Simses and the explosive Sinner Man by Roberts, Yannick Lebrun and Kirven James Boyd were particularly good. Briana Reed was magnetic leading the rollicking Rocka My Soul finale.