When Michael Burnham (Sonequa Martin-Green) first meets Captain Gabriel Lorca (Jason Isaacs), his room is dimly lit. He mutters something about an eye condition requiring low light, but, as with most of his statements, there appears to be information the captain is deliberately refusing to share.

Lorca’s lair is far from the only interior on “Star Trek: Discovery” that is shadowy. As Burnham frequently negotiates dark corridors and murky settings, one thing becomes clear: “Discovery” is trying, with some success, to convey that this is not your father’s “Star Trek.”

It might be your mother’s, if she is a fan of “Star Trek: Deep Space Nine,” which is widely considered to be the best of the “Trek” TV efforts. (To forestall nerd debates, yes, each Federation series has its merits, but “Deep Space Nine” and “The Next Generation” top most critics’ lists.)

The later seasons of “Deep Space Nine” depicted an array of conflicted characters — led by Benjamin Sisko, an African-American captain played by Avery Brooks — fighting a grinding, complicated war that sapped their energy and challenged their ethics even as it strengthened their bonds of friendship and love. It was serialized — a rarity back then for any drama, let alone a “Trek” series — and it grew more and more character-oriented over time. At first glance, “Discovery” appears to be paying some homage to the spirit of “DS9”: Ongoing story arcs are woven through the first three episodes (and clearly will continue beyond those hours), and its resourceful protagonist has as many challenges in front of her as Sisko often did.

Of course, “Discovery” has yet to prove itself a worthy successor to “The Next Generation,” “Deep Space Nine” or “Battlestar Galactica” (where several “DS9” writers ended up after that “Trek” series ended). But there are reasons to hope that “Discovery” will be promising addition to the “Trek” canon. If it capitalizes on the conflicts at its core, and if it embraces the ambiguity and complexity baked into its DNA, “Discovery” could provide viewers with the kind of character-driven, space-set sci-fi narrative that has long been missing from the television scene. It’s early days yet, and the CBS All Access drama, which contains some wobbly elements, may let lapse into the usual array of alien-of-the-week formulas, but this voyage has potential.

The first three hours of “Star Trek: Discovery” provide serviceable space opera and reasonably exciting interstellar battles. And as a whole, the drama takes the optimism at the core of Gene Roddenberry’s vision and, in the tradition of the best of the “Star Trek” canon, uses it to examine the choices of well-intentioned characters faced with compromises, mysteries, alien cultures and moral dilemmas. “Discovery” may be set in a time of war, but it is not uniformly grim; there are some welcome comedic touches that hit the mark without detracting from the drama’s generally earnest approach.

It’s worth noting that there’s also a fair bit of the original “Star Trek” woven into “Discovery’s” premise, given that it’s set about a decade before the events of that program. Even the communicators look like the flip devices of old. But there’s one detail that unites all the “Trek” series, including this one: There are always Jefferies tubes.

“Discovery” had a difficult gestation process, and so there are a number of narrative hiccups, likely resulting from the departure of original showrunner Bryan Fuller while Season One was still being mapped out. A few plot points and character arcs don’t quite track, and some aspects of the show haven’t gelled yet. The Klingons, who are dangerous enemies in this world, are very elaborately garbed and their scenes are often ponderous and too slow (the actors give their level best, but they labor under imposing facial prosthetics that make their expressions hard to read). Another complaint: The new Federation uniforms are terrible. Why give these capable officers panels of disco-friendly gold cloth on their hips?

But relatively speaking, these are Tribbles — er, I mean, quibbles. The core mission of “Discovery” is to make viewers care about Burnham, and it succeeds in that regard. Martin-Green is charismatic and quietly forceful in the lead role, and her character is an outsider in many ways, which gives “Discovery’s” writers a lot of interesting psychological territory to explore. Her professional relationships in the present and her personal bonds from the past are mostly fraught and complicated, and “Discovery’s” handling of those aspects of her story may well determine whether it becomes must-see viewing or not. The capable cast around Martin-Green — which includes Doug Jones, Isaacs, Anthony Rapp and Mary Wisemen — all make fine first impressions.

Though her parents were human, after their deaths during her childhood, Burnham was raised by Spock’s family on Vulcan. Though she’s energetic and steadfast, she’s not quite as comfortable in the Federation or even among humans as some of her fellow crew members. It remains to be seen whether her African-American identity will be mined for storytelling purposes. “Discovery” hesitantly brings it up once, before quickly dropping it. It would be intriguing — and timely — if “Discovery” explored that aspect of Burnham’s experience now and then, instead of assuming, as “Trek” so often blithely has, that in the future humans will live in a post-racial society.

We don’t at the moment, and that’s just one reason why it’s a real joy to see an African-American woman and a woman of Asian descent (Michelle Yeoh’s Captain Philippa Georgiou) charging through the universe — leading, strategizing and kicking ass when necessary. Though “Discovery” has a number of patches of leaden exposition, the mentoring relationship between the two women is nicely sketched out by Yeoh and Martin-Green.

But it’s the moral murk that Burnham must wade through that gives “Discovery” its tantalizing possibilities. Once the set-up is out of the way — and that takes most of the first three episodes — it will be interesting to see whether new showrunners Gretchen J. Berg and Aaron Harberts will be able to capably capitalize on the ethical and personal dilemmas inserted into the premise during Fuller’s tenure (his name is among those getting story or script credits in the first two hours).

If “Discovery” builds on the best parts of its opening hours, Burnham will continue to be thrown into situations that have no easy answers and will be given missions that will bring about challenging consequences. It also remains to be seen whether “Discovery” will drive subscriptions to CBS All Access, where episodes will arrive weekly. (The hourlong premiere airs on CBS Sunday; that episode and the second installment hit CBS All Access Sunday night, and “Discovery” outings arrive on the subscription service weekly thereafter.)

“Trek” has been off the air for a while, and the strategy of reviving the TV franchise via CBS All Access is not without risk. And within the world of the show, the Klingons’ philosophy is dark — a new leader rises whose philosophy could be summed up as “Make Kronos Great Again.” But the tenacious drive that Martin-Green brings to her character’s quest to prove herself means no one should count out the Federation just yet.