Lloyd's Names have increased their commitment to Lloyd's during 2004.
For the 2004 account, private capital has risen to £3.3bn.
In 2002 it was £2.8bn, and 2003 it increased to £3bn.
Overall Names total market capacity has risen from 20% in 2003 to 22% for 2004.
The average capacity of each private capital member underwriting in 2004, excluding collective conversion vehicles, is £1,024,000, up from £790,000 in 2002 and £951,000 last year.
Three quarters of members still trade with unlimited liability.
Private members have also said that the work of the Lloyd's franchise board has made the market attractive
Association of Lloyd's Members (ALM) chairman Michael Deeny said: "The current profitability of Lloyd's will enable Names to recover some of the heavy losses they have suffered in the past.
"They are encouraged by the important changes being made at Lloyd's, which should improve its ability to manage future challenges."