Coping with success isn’t a bad problem for a TV show to have. It can still be a problem.  

Killing Eve, whose second season premieres at 8 p.m. ET Sunday on both BBC America and AMC, snuck up on audiences last year and won them over with its skill at making a psychokiller show also feel like good fun.

For want of a more precise descriptive phrase, Killing Eve became a female buddy tale, in which cold-blooded assassin Villanelle (Jodie Comer) and her neurotic pursuer, MI5 agent Eve Polastri (Sandra Oh), developed a mutually torrid obsession.

The premise of attraction between the fox and the hound isn’t unprecedented, having recently enjoyed a good run with two guys in The Following. The difference in Killing Eve lies in the light touch with which it handles Villanelle’s work and Eve’s response.

Villanelle doesn’t only seem to kill people who need killing, as the line from Westerns used to go. She’s fine with killing men, women, children and anyone else who’s either a target or simply inconvenient.

She seems to have no spark of feeling, remorse or even acknowledgement that her work has any more emotional resonance than weeding a garden.

At the same time, she’s witty and clever, which isn’t always the same as having an actual sense of humor, but does allow her to joke about, say, her confidence and skill in the killing machine game.

Eve, meanwhile, is by most standards a wreck. Her people skills can be as ragged as her eating habits.

She’s also smart. And intuitive. She put the pieces of Villanelle killings together in a way that others in the agency couldn’t see, which is how she got onto the case.

That said, Eve was fortunate Villanelle didn’t simply whack her up front, since compared to the clever, wary people Villanelle had killed in the past, Eve was a turtle in the middle of a six-lane highway, just waiting to get run over.

But Eve survived long enough for Villanelle to decide she presented a respectable challenge, by which time each had become fascinated with the other.

It wasn’t the sort of development that could be easily explained either to Eve’s boss Carolyn (Fiona Shaw) or Villanelle’s handler Konstantin (Kim Bodnia).

It was, however, lots of fun for viewers.

Then, in a final twist, the season ended with Eve stabbing Villanelle and fleeing in panic, fearing Villanelle was dead.

Which would have been fine with law enforcement and not so good for the show. That is to say, it’s not a major spoiler to reveal that Villanelle starts the second season 30 seconds later and not dead.

The first episode of the new season cuts back and forth between Eve and Villanelle, with each behaving in ways consistent with the first season. Even innocents aren’t always safe around Villanelle, while Eve acts like a woman who’s off her meds.

Still, Killing Eve doesn’t feel quite the same, and one does wonder if success has created pressure.

When the show developed the kind of following and buzz that lifted it past cult-fave status last season, there were two clear and obvious reasons.

First, a female assassin with mad skills and an attitude closer to James Bond. Second, a law enforcement agent with Sherlock Holmes-like powers of deduction and Inspector Clouseau-like levels of neurosis.  

It wouldn’t be surprising if the writers and producers wanted to ratchet those winning qualities up in Season 2.  

What if Villanelle were to develop even greater powers of manipulation and evasion? What if she were to take deadly advantage of the most vulnerable and sympathetic character around?

What if Eve were to melt down almost into a puddle of doubt, then suddenly snap back into a moment of brilliance as if nothing had happened?

What if Villanelle’s dry wit became drier, and she became even more confident with how her chess match with Eve would play out?

Maybe you’d get a second season with more of what sold the first season.

Conversely, you might start parodying yourself, making these women into animated characters from a graphic novel.

That wouldn’t necessarily be bad. It’s just not why we were drawn to them in the first place. Killing Eve has dealt itself a fine hand that it must be careful not to overplay.