Anthony Watson, chairman of the remuneration committee at Lloyds, owner of Bank of Scotland, told the Association of British Insurers investment conference that non-executives on the boards he serves on have sought to hold down basic pay to keep a lid on related bonuses.
Mr Watson, a former fund management executive, added: "It is surprising how many remuneration committees do not know, when they sign off the plan, how much the variable pay is going to be."
Mr Watson, who is also a non-executive director of property company Hammerson, mobile phone operator Vodafone and Witan Investment Trust, said of executive pay: "I do think things are getting better."
"In those [companies] I am involved with we are trying very hard to stop variable pay morphing into fixed pay which is the precursor to pay for failure."
But the former chief executive of Hermes Pensions Management criticised a focus on how much a chief executive takes home.
"It really doesn't matter whether or not you double or halve the pay of the chief executive," he said; rather, the focus should be on the size of the overall bonus pot versus returns to investors.
John Stewart, the Scot who chairs insurer Legal & General, said there has been a tendency for companies to compensate executives whose long-term incentive schemes are not paying out by giving them higher short-term bonuses.
The former chief executive of National Australia Bank, owner of Glasgow-based Clydesdale Bank, said even a small shareholder rebellion can spark a change of policy. Mr Stewart added: "You only need to register 10% as a protest and we will pay attention."