US catastrophe rates have risen by only 20% on average, against the industry's predictions of 25% to 35%, said a reinsurance expert.
Catex European managing director, Tom Bailey, told Insurance Times that the new Bermudan start-ups had slowed the market because the companies did not have any historic losses to recoup and needed to attract business.
"Their impact is to take some of the business from London and to reduce the hardening affect of 11 September.
"It is not inconceivable that the increased capacity will cause pressure on rates going forward," Bailey said. "We are seeing evidence of that already, which would throw us into a soft market."
Since the World Trade Centre attacks, new reinsurers such as Axis Specialty have rushed to take advantage of massive rate rises.
There are now about ten start-ups based in tax-free Bermuda, backed by between $500m to $1bn (£354m to £709m) each.
Last week Olympus Re and Queens Island Re became the latest ventures to be registered.
Fitch ratings senior director of insurance, Gregson Carter, said: "We are now back to appropriate pricing levels but not back at real bumper market excessive profit."
Standard & Poor's director of financial services ratings, Rob Jones, said the consequences of the Bermudan start-ups will be felt at the next renewal period in July.
"They are going to have a longer term impact on pricing," he said. "This will mean the cycle will turn earlier than it would otherwise have done."
But Carter added if World Trade Centre losses were worse than originally predicted, rates will remain high.
