When you’re writing a hard-boiled mystery series with a tragically stoic protagonist — a significant chunk of the television market these days — a little comic self-awareness is a valuable commodity.

“It’s never straightforward with you, is it, Jack?” a friend asks the eponymous hero of “Jack Irish,” after what looked like a traffic accident turns out to be a homicide with ties to academic fraud, drug dealing, dirty immigration agents and big pharma. “Never just a meat-and-three-veg murder?”

“Jack Irish,” an Australian series whose second six-episode season goes up at Acorn TV on Monday, is in the same general category as Amazon’s “Bosch” (based on books by Michael Connelly) and “C.B. Strike,” the BBC-Cinemax adaptation of J.K. Rowling’s mystery novels. That is, it’s a straightforward, noirish mystery starring a laconic, mostly noble, unapologetically genre-friendly gumshoe. (The first “Irish” season and three previous TV movies, all available at Acorn, were based at least in part on novels by Peter Temple, who died in March; the new season is original.)

The show is set apart, though, by its sense of humor, a quality that’s usually rationed in TV mysteries these days to preserve an overall (and often suffocating) atmosphere of seriousness. “Jack Irish” isn’t unserious — there are grisly deaths and beatings, and the incident in the first movie, “Bad Debts” (2012), that threw the high-flying lawyer Irish off the rails and into a life as a bagman and part-time private eye was unusually savage.