Northern Ballet Theatre, Lyceum Theatre, Sheffield

A rhapsody in popular ballet

What's in a name? A hell of a lot, as every marketing department knows. The name I Got Rhythm, tagged with the promise of "The Genius of Gershwin in Song and Dance", has ensured a scramble for tickets all along Northern Ballet Theatre's touring route. In its debut week, Sheffield scrambled so energetically – sight unseen, opinions unreported – that it was sold out. It was touch and go as to whether the company could shoehorn me in.

I'm so glad they did, because I Got Rhythm, originally made for BalletMet in Ohio, is an ideal acquisition – as is its choreographer, David Nixon, NBT's new director. First Madame Butterfly, now this: Nixon manages to attain popular appeal without tawdry populism. His subject matter shows box-office instinct but his treatment refuses to underestimate the public's intelligence. It's ballet to suit audiences across the board.

If you like George and Ira Gershwin – and who doesn't? – this is the show for you. The favourites are all there: An American in Paris; Rhapsody in Blue; songs from Porgy and Bess, Lady Be Good and Girl Crazy. NBT's expanded orchestra, directed by John Pryce-Jones, includes singers and Jonathan Scott as solo pianist. They sit, spotlit, in a semi-circle on stage, against a star-pricked night sky. If you like traditional ballet, you will be delighted by the choreography, which proves that classical steps carefully spiced with Broadway moves can look right allied to jazz.

The excellent Liz Zengara and Jim Orrante, guesting from the BalletMet cast, led the elaborate ensemble for Cuban Overture. The dancers divide into unusual, witty groupings, although you might have wished for more pep and sexiness from NBT's men. Similarly, Pippa Moore needed to phrase her solo to the first of the Three Preludes with even more slinky playfulness; but Daniel de Andrade was ultra-suave when he later partnered her in complex, twining lifts. Christian Broomhall and Simon Kidd were equally good, conveying charm without stickiness in the title song – a clownesque duet, with tap postures and exhausting jumps that leave them collapsed at the end.

Nixon is not only fluent, he keeps everything fresh with unexpected, but apposite touches, such as De Andrade as Desiré Samaai's kneeling partner for "Bless You is My Woman". A chorus line of high-kicking men and women to a medley from Girl Crazy contrasts with the men's ballet-classroom tours en l'air in the same number. And "Summertime" is the cue for a female group-dance that shines with lyrical simplicity.

If you are worried about songs being sung by fourth-rate singers with fake accents, worry no more. Simone Sauphanor and Barry Martin are Trinidadian performers with fabulous voices. From every angle – song, music, dance and nighttime glamour (Nixon also designed the costumes) – I Got Rhythm is magic.

Marlowe Theatre, Canterbury, 5-8 June; New Theatre, Cardiff ('Madame Butterfly') 11-15 June; Grand Theatre, Leeds, 18-22 June; Theatre Royal, Bath ('Madame Butterfly') 25-29 June