The Desert Star Playhouse’s new show — called “How the Grinch Saved Christmas” and “The Grinch Who Saved Christmas” on the press release, and simply “Grinch: A Parody” on the program — has just the right blend of yuletide sentiment and plain ol’ wackiness.

It is more a retelling (with some alterations) than a parody of Dr. Seuss’ “How the Grinch Stole Christmas.” The hirsute title character (played by Paul Thomas Murphy) lives on a mountain above Whoville, hates Christmas, tries to steal it, etc. He is accompanied by his faithful talking dog Max (Scott Holman, who also directed), who serves as his conscience and straightman.

There are three kids who try to thwart the Grinch: adorable Cindy Lou Who (Kerstin Anderson), know-it-all Becky Sue Who (Holly Braithwaite) and bratty brother Sam Who (Steven Fehr). Their widowed mother (Kathleen Richardson; double-cast with Arika Schockmel), who doesn’t believe the Grinch exists, is being hit on by the creepy mayor of Whoville (Spencer Ashby) and Hunter Who (Jack Drayton), the dashing stranger who offers to rid the town of its Grinch problem.

The first scene is grossly over-full with sub-sitcom jokes, mostly from the kids. (Example: “Mother said there’s no such thing as a Grinch.” “Yeah, but she also said it won’t hurt to go to the dentist.”) The show should be parodying the too-cute kids you see in Christmas specials, not including them.

The humor improves after that, thanks largely to the Grinch and Max. I was particularly fond of the Grinch as an incompetent Santa Claus (“He, he, he!” he laughs), and of Max’s accidentally disguising himself as Adolf (as in Hitler) instead of Rudolph (as in the red-nosed reindeer). Spencer Ashby also earns some laughs as the fatuous mayor.

The show has the Desert Star’s usual assortment of random showtunes. This time, songs from “Mame,” “Oklahoma!,” “Gypsy” and “Man of La Mancha” are among those appropriated and rewritten. A Grinch breaking into song is almost automatically funny; his dog doing it, too, and pulling a microphone out of the wall to boot, is ever better.

Should you go? Though the writing’s a bit sloppy here and there, it is holiday cheer the whole family can enjoy.

It was around this time that I discovered a fun new pastime at Desert Star: identifying the musicals from which the parodies are borrowed. I get stumped now and then, but if my friend Luscious Malone is along, she can usually fill in the blanks.