Discussing the C minor Mass in a booklet interview, Paul McCreesh remarks that ‘any attempt to complete it runs the risk of negating the quality of what survives’. Most editors and performers agree, confining themselves to the sections Mozart actually composed, and filling out the missing parts in the Credo, ‘Et incarnatus est’ and Sanctus-Osanna. Enter American pianist-scholar Robert Levin, who having made arguably the most convincing realisation of the Requiem, has now provided a completion of Mozart’s most monumental score.

His work is inevitably more ambitious and, just as inevitably, more controversial than his Requiem edition. For two of the sections left uncomposed by Mozart – the jaunty ‘Et in Spiritum Sanctum’ and the beautiful, dark-coloured Agnus Dei – Levin, reasonably enough, draws on a two-part soprano aria from the Italian cantata Davide penitente (K469). Most of the cantata recycles music from the Mass; here, and at the end of the ‘Cum Sancto Spiritu’ fugue, where Levin incorporates the florid vocal cadenza added for the cantata, the compliment is returned.

In the opening section of the Credo, incompletely realised by Mozart, Levin’s brass scoring is the boldest and most effective I have heard. Elsewhere, in the missing sections, he elaborates a few fragmentary sketches to produce plausible, if hardly inspired, Mozart pastiche. The ‘Crucifixus’ is an eight-part stile antico fugue, finely worked but dour in effect (Mozart, you feel, would have engineered something more dramatic), while the ‘Et resurrexit’ and the fugal ‘Dona nobis pacem’ (based, like the ‘Crucifixus’, on Mozart’s sketched fugue subject) recall the jolly bustle of the composer’s Salzburg Masses. You could argue that these stylistic incongruities are all of a piece with the eclecticism of the C minor Mass. But several hearings have not altered my initial reaction that the final sections of the Credo and the ‘Dona nobis pacem’ are a serious anticlimax after the sublimity of so much that has gone before.

Still, Mozart lovers who want to sample Levin’s skilful and scholarly work for themselves will feel pretty well served by Rilling’s performance. Except for the odd patch of tired soprano intonation, the chorus is incisive, athletic and amply weighty; the orchestral contribution is equally vivid (splendid louring horns and trombones in the massive ‘Qui tollis’, for instance); and though Rilling at times (say, at ‘Et in terra pax’) favours a disconcertingly clipped, marcato style, he chooses generally lively speeds and builds the monumental movements powerfully.

Only once, in a languorous ‘Et incarnatus est’, is his choice of tempo unconvincing, though if you can accept a distinctly romanticised approach, Diana Damrau sings this beautifully. In the ‘Laudamus te’ and the ensembles Juliane Banse deploys her deeper-toned soprano with style and sensibility, even if her top As and B flats can take on an abrasive edge. The recording gives the choir plenty of impact while never obscuring important orchestral detail.

Paul McCreesh and the French conductor Emmanuel Krivine give us the familiar torso in readings that combine a smallish chorus numbering around 30 with a period-instrument band. Krivine has two appealing soprano soloists in Sandrine Piau (though I don’t care for her habit of crescendoing into notes in the ‘Et incarnatus est’) and Anne-Lise Sollied. They are delightful in their celestial sparring in the ‘Domine Deus’ duet, done rather more delicately than usual. At a slightly more urgent tempo, McCreesh’s soloists, the radiant Camilla Tilling and the rich-toned Sarah Connolly, are just as good, with Connolly unfazed by her flights into high soprano territory.

Elsewhere, Tilling perfectly catches the wondering pastoral innocence of the ‘Et incarnatus est’, taken at a gently lilting two-in-a-bar. In the choral numbers McCreesh wins hands down over Krivine, whose beat tends to plod (try the opening of the Kyrie) and whose sopranos too often sound underpowered and under the note.

There have been excellent period-instrument recordings from Hogwood and Gardiner. McCreesh, sharply responsive both to the Mass’s neo-Baroque monumentality and its Italianate sensuousness, is at least their match in drama and colour; and DG’s recording is exemplary. The Gabrieli Consort sing with precision, fresh, firm tone and marvellous dynamic control, while the strings play with notable grace and refinement in the solo numbers. The Kyrie unfolds with an inexorable tread (McCreesh is specially good at creating and maintaining rhythmic tension), and the ‘Cum Sancto Spiritu’ fugue, taken at the swiftest possible tempo, combines dancing agility with a thrilling cumulative sweep. McCreesh’s claims as a top recommendation are enhanced by the additional items, two magnificent, quasi-operatic scenas by Haydn and Beethoven. Connolly, in the Haydn (again taking the high tessitura, complete with top Cs, in her stride), and Tilling are both superb, marrying a classical nobility of line with a profound identification with the plights of these suffering heroines in extremis.