It would seem to be an impossible task.

How could two writers take one of Shakespeare’s “problem plays” and have no problem turning it into a wildly successful musical comedy?

After all, MEASURE FOR MEASURE starts out pretty grim. Claudio impregnated Juliet before they could finish the paperwork that would allow them to marry. This cuts not a shard of ice with the oh-so-devout Judge Angelo, who sentences him to decapitation.

Enter Isabella, a sister in more ways than one: Claudio’s sibling as well as a nun.  She implores Angelo to pardon her brother and indeed he will – if she’ll sleep with him.

And you thought hypocrites of Jimmy Swaggart proportions were something new. No, and the attitude of a person in power is that “the law doesn’t apply to me” has been around longer than the 400-plus years when Shakespeare wrote his play.

However, Isabella is truly religious, and won’t succumb no matter how much Claudio begs her to save his neck and head. A Duke on sabbatical makes a suggestion that suddenly turns an increasingly dour play into a farcical one — which is why the scholars call MEASURE FOR MEASURE a problem play.

You know Shakespeare and his penchant for mistaken identity. The Duke suggests that Isabella agree to meet Angelo in his boudoir; then, after all the candles have been extinguished, Isabella will high-tail it out and Angelo’s on-and-off-again girlfriend Mariana would slip between the sheets and pretend to be her.

This inordinate amount of time spent on MEASURE FOR MEASURE is meant to show what bookwriter-lyricist Peter Kellogg and composer David Friedman wisely kept and shrewdly discarded to make DEPERATE MESURES a delicious concoction. It’s at the York Theatre Company through the end of this month, but here’s hoping that the funniest, most tuneful, non-stop, slam-bang best musical of our four-month-old season will soon move to the Westside Theatre or New World Stages and stay for four or so years.

(It’s got merely one set, six performers and four musicians. Come on, producers — what are you waiting for?)

Kellogg moved DESPERATE MEASURES to the Wild West in the late 1800s. This gave Friedman the opportunity to write music that mixes country with his native Broadway sound. He’s completely succeeded.

Claudio the sex-fiend is now Johnny, who killed in self-defense. Still, the Governor will have him hanged, partly to aggrandize himself with his Arizona constituents. “They will capture me,” he sings — a lyric that seems to make no sense until we realize that we haven’t heard the last of it: “in bronze,” he adds.

Isabella is now Sister Mary Jo — not yet An Official Nun, but one in-training. Even her somewhat casual name – nuns of that era usually had austere ones: Sister Mary Alcantra, Sister Mary Marillac — suggests that Novice Mary Jo could still Maria-von-Trapp herself into a relationship.

Sheriff Green wishes she would, for he’s quite smitten with her. True, Shakespeare thought of linking Isabella and Angelo, but didn’t do as much with the situation as Kellogg has.

Although Sheriff Green isn’t as jealous as Othello when he hears Sister Mary Jo is going to go at it with the Guv, he isn’t pleased. He doesn’t know that she actually won’t, what with Bella Rose taking her place.

If Bella were living in the era of income tax, she’d list her occupation as Bargirl/Entertainer rather than reveal that the way she makes most of her money is precisely the manner that Xaviera Hollander and Fanny Hill made theirs. The best joke of the night comes when Bella is told that to pull off the ruse she’ll have to dress as a nun – to which she blithely says that she already owns a habit because certain customers demand that she wear one.

If Shakespeare were alive today, he might smack his head for not thinking of a romantic entanglement that Kellogg did: Johnny is in love with Bella, who promised to give up her wayward ways for him. Now, though, she’s ready to do it with the Governor (not, however, that she hasn’t done it with him already, as she’s not too shy to mention). Moans Johnny when he hears the plan, “All this saving my life is killing me.”

As if creating perfect rhymes for 16 songs wasn’t enough of a challenge, Kellogg raised the considerable bar for himself by deciding to write the book in rhymed iambic pentameter. So we not only get the chance to savor what rhyme might come next in song – and many are splendid — but also in the dialogue.

Kellogg’s jokes get laughs that are substantially longer than the theatrical average. Subtle gags abound, too. When The Governor says he was so surprised with Isabella’s performance in bed, she responds “That woman last night was not the real me.” We don’t expect a nun to lie, and God knows she hasn’t.

Even costume designer Nicole Wee gave some extra thought and inspiration when creating Sister Mary Jo’s nun’s habit. A by-the-book costumer would have put her in standard-issue black without a thought to anything else. She looks so much more vulnerable and innocent in a benign combination of white and blue — colors long associated with The Virgin Mary.

From the first moments — when Johnny’s victim wears a patently false mustache — director Bill Castellino sets a tone where a tongue isn’t firmly planted in cheek, but rubs against it a little. How lucky he was to find newcomer Emma Degerstedt for Sister Mary Jo. She is loveliness personified and yet, when faced with adversity, is no shrinking nunlette. Degerstedt is a young Barbara Cook, and if she leaves the show during its deserved four-year run, here’s hoping it’s to star in The Music Man or She Loves Me.

Nick Wyman is excellent as the Governor, using a Germanic accent befitting his last name: Richterhenkenpflichtgetruber. (All right, that’s over-the-top unbelievable and unnecessary.) Actors are always looking for subjects they can play in one-person shows; Wyman is a natural for one on Bela Lugosi. (And he has four years to write and develop it, because – well, you know.)

The rest are swell as well: Lauren Molina gives Bella that requisite heart-of-gold that shows a little tarnish. As Johnny, Conor Ryan amuses in his agony. As brave, courageous and bold a sheriff as Wyatt Earp has been said to be, Peter Saide is all that while being much funnier. Gary Marachek keeps the faith as Father Morse, who doesn’t restrict his drinking to communion wine.

Although the songs that Kellogg and Friedman penned are winners, they dared to write encores for a couple, which is always a dangerous practice; what if the applause that greets the song proper is only polite and indicates no encore need apply? That doesn’t turn out to be an issue here. The audience coos with pleasure when the band revs up as they relish the chance to hear a few more bars of the song they’d just savored. May 1,664 future off-Broadway audiences have the same experience.