After causing so many problems last term, Tevez seems to be a much more settled figure nowadays.
He even wandered to the touchline for a bit of advice from manager Roberto Mancini during yesterday's 3-2 win over newly-promoted Southampton, something unimaginable during the middle of that war of words which resulted in him spending a large chunk of last season away from City's Carrington training ground.
Now Tevez looks like the player who became such a Blues hero after his move from Manchester United in 2009.
And with City anxiously awaiting news on the extent of Sergio Aguero's knee injury, Tevez could be a crucial figure in the defence of the Premier League.
"Carlos is recognised by everyone as one of the best strikers in the world," said Kompany.
"People talk about new signings but having Carlos at his best level, which he wasn't last season because he was away for most of it, is just like one.
"I still say we have improved.
"If we were to lose Sergio, it would just go back to last season. Other players would have to step up and perform. They have always done that."
Kompany does not want to dismiss Aguero just yet, even though Mancini's body language immediately after yesterday's [Sunday] game suggested he expected bad news later this week.
That could force a renewed attempt to bring in additional firepower, although with UEFA's Financial Fair Play regulations to meet, City have an equal need to get rid of their unwanted high-earners, including Emmanuel Adebayor and Roque Santa Cruz.
Kolo Toure and Nigel de Jong are two others who seem surplus to requirements, although in the latter man's case, Gareth Barry's present injury problems may bar the exit door.
The one new face introduced by Mancini this summer is Jack Rodwell.
And though the former Everton man was at fault for Southampton's second goal yesterday, considering he only signed for City seven days previously, and had been involved in just two training sessions with his new team-mates, Kompany believes there is every reason to be satisfied.
"Jack has settled in really well," said Kompany.
"His performance was ahead of what you would have expected from someone who just came in for his first game after two training sessions.
"Maybe it was the right moment to introduce him. In any event, it paid off.
"Now the tough games come and I am sure we will gain a lot from having him with us."
City face an even stiffer test next Sunday when they visit a Liverpool outfit smarting from that stunning defeat at West Brom on Saturday.
The Blues beat their Merseyside rivals just once in four attempts last term, and drew a testy affair at Anfield in November, when Mario Balotelli was sent off.
"Playing at Anfield has never been easy," said Kompany.
"They have always been very difficult, intense games.
"They will fancy their chances. But we fancy ours as well."
And, as Kompany outlined, City's attitude has changed with their champions tag.
Now they have additional self-belief, so even in tricky spots, like they encountered against Southampton, there is a certainty they will eventually come through.
"We are just doing what we did last season - try and win as many games as you can," he said.
"But the moment we went 2-1 down, we did all have a feeling that we weren't going to lose.
"Don't ask me how, we just felt we weren't going to lose. Then it just happened for us.
"I would have liked to be safe a bit earlier but it is great that we have that character."