Barclays chairman Sir David Walker cited as an example of progress that there is now a "tetchy" atmosphere in Barclays' boardroom.
But the bank refused to comment on reports it had given the Qatari Government a multi-billion-pound loan, which it then used to recapitalise the bank at the height of the financial crisis.
Despite the renewed focus on the bank, and the announcement that it has made another £1 billion of provisions for mis-selling compensation, Barclays' shares closed up 3.75p or 1.3% at 295.25p.
Giving evidence to the Parliamentary Commission on Banking Standards, Mr Jenkins said: "In the past 20 years there have been circumstances where I believe we have been too short-term focused, on occasion too aggressive and on occasion too self-serving.
"It is these that I would like to eliminate from our culture."
Appointed in August following the sudden departure of Bob Diamond after the bank was fined for manipulating Libor interest rates, Mr Jenkins came under pressure, particularly from Archbishop of Canterbury Justin Welby, to justify how continued high pay for top staff was consistent with reform.
Mr Jenkins said: "I am not sure in my business as opposed to your business whether we would attract people who would be willing to work for one-tenth of what they might receive somewhere else."
Mr Jenkins said bonus awards for last year would be cut.
Sir David, who replaced Marcus Agius in the wake of the Libor scandal, insisted that Barclays now has a more robust board.
"We have in the Barclays boardroom a rather tetchy atmosphere and I rather like that," he said.
Asked about accusations that the Serious Fraud Office and the Financial
Services Authority are investigating whether Barclays lent Qatar funds to buy shares in the bank, Sir David said: "Unfortunately, we are not able to comment on it."
The purchase of a stake by Qatar allowed Barclays to avoid following Royal Bank of Scotland and Lloyds Banking Group, owner of Bank of Scotland, in taking a Government bailout.
It was revealed last week that Mr Jenkins is not taking a bonus for 2012.
The decision came after the bank was embroiled in scandals surrounding the fixing of Libor, and the mis-selling of interest rate swaps and payment protection insurance.
Commission chairman Andrew Tyrie told Mr Jenkins and Sir David: "It doesn't seem to matter what the scandal is, Barclays seems to have a finger in each pie, quite a big one,"
Barclays has increased its provision for redress for interest rate swap mis-selling by £400m to take the total it has put aside to £850m.
The bank has also put another £600m aside for PPI compensation.
This, it said, was due to higher than expected response to letters sent out at the end of last year.
It has made a total provision of £2.6bn for PPI redress, of which it has paid out £1.6bn.
"This (Barclays' provision) is by far the highest among UK banks and suggests further provisions by RBS, Lloyds and HSBC," said Shailesh Raikundlia, analyst at Espirito Santo.