●“Elementary” (premieres at 10 p.m. on CBS). Sherlock Holmes gets his zillionth update, this time with Jonny Lee Miller (“Eli Stone”) playing Arthur Conan Doyle’s timeless sleuth as a recovering addict whose British tycoon father ships him off to Manhattan for rehab.

Lucy Liu plays Dr. Joan Watson, a disgraced former surgeon who’s been hired to act as Sherlock’s 24-hour sober-living companion after his detox. In almost no time at all, they are working together on a murder case after Sherlock is asked by a New York homicide detective (Aidan Quinn) to examine a tony uptown crime scene.

In a way, CBS is honoring its present-day success as crime-procedural central with this twist on the daddy of all detective serials. “Elementary” exhibits enough stylish wit in its mood and look to quickly distinguish itself from the latest British “Sherlock” series (seen on PBS), in which Benedict Cumberbatch (or Bandersnatch Cummerbund, as my colleague Lisa de Moraes likes to call him) plays a far icier version of the character. Miller’s Sherlock is just as ludicrously smart and socially callous, but he’s scruffier and more vulnerable. And as Watson, Liu seems to know exactly what’s she’s doing. There’s no reason this show can’t succeed, so long as the writers find a way to deal out more complex mysteries that are worth Sherlock’s time. Grade: B+