The American outfit went through a demoralising 2023 campaign in which Nico Hulkenberg and Kevin Magnussen couldn't convert reasonable one-lap pace into race results, due to its car eating through the Pirelli tyres on most circuits.
Haas never found a solution to raise its performance level and after finishing bottom of the constructors' championship, a result which led to Guenther Steiner's exit as team principal, it was cautious about its prospects to fare better in 2024.
But it proved more competitive at last week's season-opening Bahrain Grand Prix than expected, being in the hunt for points with fellow midfield outfits Sauber, RB and Williams.
While Haas was finally able to race others without battling extreme tyre drop-off, Steiner's replacement Komatsu has cautioned that its Bahrain form doesn't mean tyres are no longer an issue.
"I wouldn't say we completely got over it," he said. "We got much better handle on it and then we have a car that is much more consistent, so that helps.
"But our race pace is still weaker versus our qualifying pace, so we still got work to do on that."
Bahrain is notoriously abrasive and demanding on tyres, which could be a positive sign that as Haas survived there, it can be more competitive on various other circuits too.
But the unusually cool temperatures at Sakhir last week mean there are still some lingering question marks.
"Bahrain is hard on tyres, the track is very rough and it's rear limited, traction is pretty difficult," Komatsu explained.
"But it wasn't as warm as normal years and it's an evening race as well. Here [in Jeddah] is a different downforce level and higher speed corners.
"When you go to places like Suzuka with more medium to high speed corners, that will be a different challenge too.
"So, I don't think we are completely on top of it. I'm happy with the progress we made, but we really have to stay focused and make sure that we stay on top of it for various different circuits and conditions."
Hulkenberg's Bahrain race was derailed by contact at the start, while Magnussen finished on the tail of 11th-place finisher Zhou Guanyu in the Sauber.
Matching Aston Martin, the fifth-fastest team so far, appears a step too far for 2024's bottom five squads but Komatsu reckons the fight among them, which yields points depending on how many faster cars hit trouble, is still too close to call.
He said: "It's really depending on the circuit. We've only done one race and here with the different downforce level, different speed of the corners, longer straight, it's going to change.
"Only after four or five races we get the bigger picture, but it's all very tight."
