Lloyd's insurer Amlin has launched plans to raise £80m in a placing and open offer of shares.
It will use the money to try to buy out one of its syndicates.
Investors will be able to buy 13 new shares at 81p each for every 67 they already own.
Amlin's shares were selling for 87p on Tuesday afternoon. They were down by 2.5p or 2.8% after the company increased its estimate of the net loss it will suffer from the WTC attack to £65.5m.
Its estimate in the immediate aftermath of the event was £45m. The loss stood at £63.9m by the time it produced its annual report and accounts in April.
Finance director Richard Hextall said the estimate was now reasonably stable and stock markets had more confidence in insurance than earlier in the year, when Amlin sold stock to raise £43m.
He said: "The markets are more open now to insurance than they were at that point. There's more certainty and our own insurance markets are demonstrating they have improved."
The company aims to use the money it raises in the sale of shares to increase its ownership on Lloyd's Syndicate 2001 to 100% from 72.3%, giving it a bigger share of any profits.
But any purchase will depend on Amlin persuading Names to sell their capacity at a time of rising profits.
Hextall said: "We will make the Names a reasonable offer, but it's their choice.
"We can utilise the capital whether or not we buy out the syndicate or just increase the capacity with Names on board as well."
Amlin has increased its books of business in property, property reinsurance and aviation as markets continue to remain hard.
Syndicate 2001 has acquired the renewal rights to about £18m of business being written by Japanese insurer Aioi's European division.
Amlin's biggest shareholder, US insurance giant State Farm, will take up about 13.5% of the shares sold in the placing as well as its full entitlement in the open offer.