Cut-and-dried network crime shows will probably be with us forever in one form or another, because they’re easy to watch and offer very little in the way of gray areas — even as viewers have become increasingly aware, thanks mainly to prestige dramas and documentaries, that the criminal justice system is far more complex, and compromised, than the fictions we grew up watching.

That’s why we tend to applaud any attempt to offer a new read on the old formats, as John Ridley did five years ago with his “American Crime” anthology series for ABC. That show may have only lasted three excellent seasons, but its influence is felt anytime a creator pitches a crime story that’s told from an overlooked perspective. Two new prime-time dramas arriving this week and next — CBS’s “Tommy” and ABC’s “For Life” — may not be that impressive, but they come across with fresh, and at times suitably compelling, premises.

In “Tommy” (premiering Thursday), Emmy winner Edie Falco (“Nurse Jackie,” “The Sopranos”) stars as Abigail Thomas, a high-ranking New York police officer who has just been named Los Angeles’s newest police chief. She’s the first woman to hold the job, and she insists that everyone just call her Tommy. A reluctant and connivingly smarmy mayor (“Life in Pieces’s” Thomas Sadoski) hired Tommy on a court order after her predecessor was sunk by widespread corruption and a scandal involving a sex-trafficking ring.

Facing a surf wave of skepticism, Tommy breezes into L.A. with a combination of brash outsider confidence and a disarming demeanor — as well as bellyaching, as all New Yorkers must, about a lack of decent bagels and pizza slices. She doesn’t like it when her officers rise in salute when she enters a room, and because it’s a TV show, she’ll be solving a lot of each week’s crime load herself, thanks.

“Tommy,” created by Paul Attanasio (extremely longtime Post readers may recall his film criticism from the mid-1980s, before he became an Oscar-nominated screenwriter), is far too busy, ticking the items off Tommy’s frantic to-do list. In addition to defusing a standoff between federal immigration officers and an L.A. cop trying to prevent them from arresting an undocumented mother, Tommy also gets the cold shoulder from sexist officers still loyal to the former chief.

“If I fail,” Tommy confides to one early ally, “it will be 20 years before they give another woman this job.”

Falco, of course, is the main reason to tune in, even as “Tommy” struggles to match her range, from serious empathy to dry wit. And, because we are living in 2020, the show easily glides into the rather ho-hum revelation that Tommy is a late-blooming lesbian, having divorced her husband some years ago, thereby alienating her daughter, Kate (Olivia Lucy Phillip), who lives in L.A., is having her own marital crisis and is not very pleased to see her mother.

The other reason to watch — indeed, the show’s true potential — is Tommy’s unflappable approach to good community policing, on a network that for too long has fetishized grisly murders and the wonders of DNA results. The show reaffirms CBS’s commitment over the past decade to have one, sometimes two, shows (“The Good Wife,” for example, or “Madam Secretary”) that clearly demonstrate a woman’s leadership capability in a high-pressure job, even when she’s surrounded by men giving her advice.

Although the odds are stacked against her, the consistent message in “Tommy” is one of persistent ethics, threaded with moments of doubt and vulnerability. Although much of the show’s first three episodes are powered by procedural cop stuff, I think Tommy (and Falco) could handle an even trickier balance — not so much between her job and her life, but between the law and the messier aspects of chronic injustice.

'For Life'

ABC’s “For Life” (premiering Tuesday) comes at injustice and systemic reform from the opposite direction, as a wrongfully convicted prison inmate, Aaron Wallace (Nicholas Pinnock), has spent the first nine years of his life sentence (for drug dealing) studying to become a lawyer and get the New York bar’s permission to practice. Although Aaron intends to counsel his fellow inmates, his longer aim is to get his own conviction overturned by exposing the shoddy police work and prosecuting attorneys who put him behind bars.

The show, created by Hank Steinberg (“The Last Ship”) and co-produced by Curtis “50 Cent” Jackson, is loosely based on the true story of Isaac Wright Jr., who studied law behind bars and successfully petitioned for his own release.

The bookish inmate who out-litigates the system is something of a sub-trope in prison dramas, but “For Life” seems determined not to turn Aaron into a jail-yard cliche. Like “Tommy,” the show is also structured around a weekly supply of new clients for Aaron to represent, but he doesn’t take just anybody’s case. (When Aaron agrees to work with one of the prison’s white supremacists, another inmate admonishes him: “A hundred brothers asked you to take their case, and you workin’ for Adolf?”)

As with Falco’s Tommy, the true reformer here is a woman — the prison’s newly installed warden, Safiya Masry (“Game of Thrones’s” Indira Varma), who sees Aaron’s cause as a worthy means to demonstrate to inmates that she respects their dignity and rights. Inconveniently, the warden’s wife, Anya (Mary Stuart Masterson), is a prosecutor angling to become attorney general, running against the same prosecutor who so zealously put Aaron behind bars.

Safiya walks a thin line between supporting Aaron and cautioning him from taking on the prosecutor in the media. Pinnock’s performance gives a palpable, urgent quality to Aaron’s intensity as both a prisoner and an attorney, outraged at a corrupt system and longing to return to his wife (Joy Bryant) and teenage daughter (Tyla Harris).

“For Life” is hampered by the formula of prime-time legal dramas, wherein the greater character studies lose out to the revolving subplots of cases, which can lead to a predictable tedium. That’s a system that also needs to be overhauled.

Tommy (one hour) premieres Thursday at 10 p.m. on CBS.

For Life (one hour) premieres Tuesday at 10 p.m. on ABC.