Shares in News Corporation have recovered ground after Rupert and James Murdoch's appearance in front of a committee of British MPs.
News Corp shares closed up 5.5% in New York and rose 5.1% in Sydney.
The move recovers some of the losses sustained as the phone-hacking scandal at its newspaper title, the News of the World, has unfolded.
But pressure on the company has continued, with more shareholders questioning the company's standards.
The giant Californian public pension fund, Calpers, has joined the list of those who are unhappy with the way the company has been managed.
Another to publicly state its unhappiness with the way the company is run is CBIS (Christian Brothers Investment Services Global Funds).
Calpers (California Public Employees' Retirement System), which owns 6.4 million of News Corp's shares, is unhappy with the shareholding structure that gives the Murdoch family's 'B' shares voting rights, meaning that although they own only 12% of the company, they hold the biggest single block - 40% - of the votes.
Other 'B' shares are largely held by unnamed investors.
More than two thirds of the shares are 'A' shares, which give investors no say as to who sits on the board, let alone major strategic decisions such as whether to bid for another company.
Calpers' senior portfolio manager, Anne Simpson, who heads its corporate governance programme, told the BBC: "News Corp does not have one share one vote. This is a corruption of the governance system.
"Power should reflect capital at risk. Calpers sees the voting structure in a company as critical. The situation is very serious and we're considering our options. We don't intend to be spectators - we're owners."
CBIS has focussed on another aspect of Murdoch power, that Rupert Murdoch is both the chief executive and chairman of News Corp.
Referring to what it calls the "egregious events" at News Corp and "eroding investor confidence" it has called on the company to separate the roles and appoint an independent chairman.
Other financially interested parties have this week reviewed their opinion of the strength of the company.
After the hearing Rupert Murdoch sent an e-mail to all News International staff.
In it he said that he and his son had appeared before the committee "to apologise, reiterate the company's co-operation with the police and explain what we are doing to resolve these issues".
The e-mail went on to say that, "Those who have betrayed our trust must be held accountable under the law."
"These serious allegations made about some of our former employees at the News of the World directly contravene our codes of conduct and do not reflect the actions and beliefs of our many employees," he wrote.
On Monday, the ratings agency Standard & Poor's placed News Corp's credit rating on a negative watch citing "increased business and reputation risks".
Also on Monday, another of its shareholders urged it to raise its standards.
The Nathan Cummings Foundation in New York, a small shareholder in News Corp, wrote to the board asking it to improve its transparency and governance:
The Foundation is concerned about News Corp's political lobbying, particularly payments to organisations that have then campaigned for looser regulation which could potentially benefit its businesses.
News Corp has reorganised its standards committee, set up to investigate impropriety at News International.
News Corporation is the parent company of News International, which runs the Sun, the Times and Sunday Times. Their sister paper, the News of the World, was shut down earlier this month as a result of the phone-hacking scandal.