The production of Die Fledermaus currently onstage at the Lyric Opera of Chicago is smart, goofy and not too fussed about keeping all its parts under tight control. That’s a good thing.

After the unremitting seriousness of Otello and Parsifal and the prim horror of La Traviata, it’s a pleasure to see the company let their hair down with this holiday favourite. The operetta by Johann Strauss Jr has tunes, dancing, infidelity, uppity maids, drunkenness and, of course, plenty of scheming. But it also has enough self-reflexivity to keep a modern audience laughing. Laughter is in no short supply in this show, and it seems to predispose audiences to be gentler on the singers. The applause flowed like champagne at a ball given by a Russian prince, anointing arias performed with varying degrees of charm.

Luckily, though, there are no real misses, as the production gathers an able cast with a surprisingly diverse range of comic style: Bo Skovhus as the randy Eisenstein, Juliane Banse as a rather serious Rosalinde, and Daniela Fally as the maid Adele. Fally has so much fun on stage you are tempted to forgive her – or director E. Loren Meeker’s – excesses, such as the second time she does the splits onstage. It starts to feel a little needy, like some triple-threater’s audition. But I wouldn’t want to lose the comic inflections she borrows from musical theater, which fit surprisingly well with her light coloratura. They set the right tone for the night.

I like Skovhus better when he’s singing than when he’s acting, as his bold, rich baritone does the work for him and keeps his hamming to a minimum. In song he is a thoroughly convincing and even moving Eisenstein, capturing a sense of nobility within the farce. Outside of song, he is, I am afraid to say, too corny even for Strauss, persisting in a Steve Martin-esque physical humour that threatens to make the whole thing a joke. Which it almost is. But you need only look at Adrian Erod’s Doctor Falke, often not far from Eisenstein, to see a man who’s funny because he doesn’t mug for a laugh. Michael Spyres is consistently hilarious as a German singer pretending, or wanting, to be Italian, which is made all the funnier because he really has an exceptional voice. That’s the key to this kind of operetta: it should be ridiculous and ravishing at once.

The other disjunctive identity is Count Orlovsky, who is played by a woman – in this case the mezzo-soprano Emily Fons. It is an especially delightful trouser role since the Count is no gasping boy but a grown man, and one who seems to have less fun at his own party than anyone else.

The sets are elegant and practical, for instance in the second act, when several layers of backdrops are consecutively raised to provide an ever-deepening visual novelty. The first and third acts both take place on stages with two levels, though this is used to far greater effect in the first. The production, which originates in San Francisco, never feels spare, but rather seems to spare no expense in creating rich textures against which the zaniness of these bumbling characters takes place.

I was both delighted and dismayed to discover the joke about the Mayor of Toronto inserted into the third act, the specifics of which you will have to discover for yourself. As a Torontonian, I can say that we are both annoyed and weirdly proud that we have become sufficiently infamous to be ridiculed so widely by Americans. To have an opera company – in a production of Die Fledermaus! – make disparaging remarks about you must surely be a sign that the bottom of the barrel has been reached. We’ll allow the joke. It is our Christmas gift to you.