What a fun feeling when two TV shows — one a returning favorite in its third season, the other brand new out of the box — start off strong.

I’m playing catch-up here, but I wanted to mention this week’s installments of “Justified,” airing Tuesdays on FX, and “Alcatraz,” airing Mondays on Fox.

In the second week of it’s third season, “Justified” continues the compelling story of Kentucky’s small-time crooks and the federal marshals who must deal with them, particularly Boyd Crowder (Walton Goggins) and Raylan Givens (Timothy Olyphant) respectively.

In Tuesday night’s episode, Givens was reunited with an old partner — and an old flame, from the sexual tension on display — named Karen Goodall. The inside joke here is that Goodall is actually Karen Sisco, a federal deputy previously played in the movie “Out of Sight” by Jennifer Lopez and — in a TV series a few years back — Carla Gugino. Like “Justified,” Sisco’s stories are drawn from the works of author Elmore Leonard.

Gugino returns to the character in “Justified” — she’s apparently signed for a few episodes — and it’s fun watching her and Olyphant kind of circling each other, particularly since Goodall/Sisco returns just as Givens is about to settle down with his ex-wife, Winona.

Tuesday’s episode — dealing with the murder of another marshal — wasn’t as strong as last week’s season premiere. But you can’t beat any show that features Olyphant, Gugino, Nick Searcy as Chief Deputy Art Mullen and Goggins.

There’s also a good introduction of Mykelti Williamson as a new character, a bad guy who is as menacing as he is folksy.

As for “Alcatraz,” I think this week’s episode, “Kit Nelson,” was my favorite so far.

If you haven’t seen “Alcatraz,” the show’s mythology is that, in 1963, the San Francisco island prison wasn’t shut down because all the prisoners were transferred. No, it was shut down because 300 prisoners and guards disappeared.

Now, a half-century later, those prisoners are reappearing, and a crew of cops and experts is pursuing them. Sam Neill, Sarah Jones and Jorge Garcia make up the solid cast of investigators.

This week’s show teased us with a little more mythology of the show. Remember Dr. Beauregard, the unseen medical officer of the modern-day prison in which Neill’s character is lodging recovered prisoners? This week’s episode revealed that Beauregard is not only Neill’s medical shaman in the present but was also the sinister doctor at the prison in the 1960s. And he hasn’t aged a day.

That little revelation, plus the beginning of a mystery involving Jones’ grandfather — a convict on the loose in modern San Francisco — and tidbits about the traumatic past of Garcia’s character are enough to allay my worries that the show might too easily fall into the “escaped prisoner of the week” trap.

And since the show is from “Lost” producer J.J. Abrams, I had to laugh when, out of nowhere, the show introduced a hatch in the middle of the woods from which a kidnapped boy escaped.

I’m not surprised to be enjoying “Justified” this much. I am a little surprised — pleasantly surprised — to be digging “Alcatraz” so much.