Pretty much from Giant Size X-Men #1, where he claws apart the tie of his commanding officer in a hissy-fit. Once Claremont got a hold of him, his original vision was that Wolverine was just one bad day away from going over the line. He famously once said that he imagined a story that would never actually be told in which the X-men would come down for breakfast and find that Wolverine had disemboweled Kitty. He also had a plan at one point for Wolverine to turn villain (in the wake of the Dark Phoenix Saga, I think?). Byrne and Miller are the ones who convinced him to soften up on the depiction of the character and explore his human side more.

I think that's backwards.

Bynre (who was the guy who really pushed Wolverine into *the* major star of the X-men, much more than Claremont) saw him as a barely controled psychopath, Claremont (and Miller) wanted him toned down and added all the samurai self control stuff.

The Claremont/Miller limited series exposed his berserker rage to poor Mariko, and we saw Logan experience shame and a deep self-loathing not previously high-lighted.

Claremont already saw him that way before Byrne. Byrne was the one who talked him out of letting the character completely self-destruct, if I recall correctly. And I'm also pretty sure it was entirely because Byrne and Wolverine were both Canadian. Still, Claremont wouldn't have had any interest in spending more time with the character, and especially not with creating a limited series with Miller, if it hadn't been for Byrne (and really, when do I EVER give credit to Byrne??). That limited series was then where we first developed strong sympathy for Wolverine and where he really developed a more purposeful self-restraint.

I think Reptisaurus's recollection is correct (aside from the extra details that shaxper added). Yes, Byrne was the guy early on who fought to keep Wolverine in the series. But it's not that Byrne wanted him nicer. Rather, Claremont though Wolverine was uninteresting until he developed more nuance.

Byrne is the more black-and-white guy and Claremont is the shades of gray guy. Byrne is more likely to think see less nuance in violence. I'm 99.9% sure that the idea about disemboweling Kitty at the breakfast table was Byrne's idea. It's important to note that it was a joke rather than something he ever intended to put in the series. But Byrne's point is that if Wolverine really has that violent pathology, killing an innocent teammate before he's realizes what he's done is something that could actually happen. Claremont is the guy who sees complexity in violence, but he often takes it to idiotic lengths. Claremont has said he likes heroes who kill, and he tries to excuse it with a cloak of nobility. Claremont wrote Uncanny #219 where Storm suggests the X-Men kill Havok simply because he stumbled upon the X-Men's plan to fake their deaths. In a sane world, that would result in the rest of the X-Men voting unanimously to ban Storm from the team for life for being a psychopath. But for Claremont it's "sophisticated" to consider the tough choice of killing an innocent person on some flimsy pretext. And let's not forget Wolverine and Rachel circa #208-209.

So:
Byrne = killing innocent people is a crazy impulse
Claremont = it's deep and mature to pretend killing innocent people could be sort of moral

The turning Wolverine bad thing was supposed to happen in the 200s, I think culminating around #300 (if Claremont had stayed with title). It was premised on the notion that Wolverine is bad. He was going to be presumed dead, and then brainwashed or possessed by the Hand or the Shadow King or someone. So it was really part of Claremont's pattern to build more stories around one of his favorites.

I always thought it was pretty funny that for someone with blades coming out of his fists, and a violent temper to go with it, you rarely got to see him cut loose (no pun intended) and do what he does best. The best example of this was in the 90s X-Men animated series. Logan would always start talking tough and pop his claws when the fighting started, but he'd inevitably get hit by weapon or explosion and get taken out of the battle pretty early. In fact, in the TV show I remember him getting his ass kicked all the time. Granted, I realize that it was a syndicated kids' cartoon, so it's not like they could actually show him skewering someone with his claws. I just thought it was funny that the solution to that was to essentially make him the cannon fodder of the team.

Off-topic, but I thought it was Psylocke (who was on the team for ... what.. 2 days at this point?) who suggested killing Havok, Storm did consider her suggestion though for a minute, but decided against it.