Cristiano Ronaldo celebrates goals with a leap and a pose — arms extended downwards, chest thrust forward — that enrage the footballer’s critics. Suggest, however, that his self-regard or pay are unmerited and you are likely to be laughed off the terraces — especially after last week’s hat-trick for Real Madrid that won the team a place in the Champions League semi-finals.

Chief executives’ assertions of their skills is even more vexing. As last week’s shareholder revolt against Bob Dudley’s 20 per cent pay rise at BP showed, tolerance for their posing is paper-thin. Investors’ impatience may erupt again at Anglo American’s meeting this week and at other FTSE 100 groups later this spring. CEOs may be paid as much as, or more than, Ronaldo, but, with vanishingly few exceptions, they are not in his league.

Excessive pay is the biggest obstacle to restoration of trust in business. This was true in 2010, when Sir Richard Lambert, then head of the CBI business association, warned it was so out of line that CEOs “risked being treated as aliens”. It is even truer now, when they have long since left our galaxy and are heading at nanocraft-speed towards the next.

No single solution will bring them back to earth. Here are four that, in combination, just might:

1) Reduce complexity. Chief executives seem just as baffled by the mechanics of complicated pay deals as outsiders are. Worse, the ambiguity of plans dulls their incentive effect. A recent report by the Institute of Business Ethics made this point using the example of BHP Billiton — the mining company reports two figures for its chief executive’s pay, one based on UK standards, the other on international accounting rules. Remuneration committees, the institute says, “often do not really know the value of what they are trying to hand over, not because they are lazy or don’t care, but because it is impossible to work out”.

2) Make transparency work in favour of restraint. Companies should always benchmark pay and targets against peers. But this can trigger the Lake Wobegon effect, where, as in Garrison Keillor’s fictional town, everyone wants to be paid above average.

Publishing pay ratios — as US companies will have to from next January — may help offset the impact, according to a study in the latest Journal of Management Accounting Research. Participants considered CEO pay less fair when told its ratio to employee earnings was many times higher than for the sector. The same perception made them less likely to invest in that company.

3) Link CEO pay more closely to actual performance, good or bad. Alex Edmans of London Business School says directors should think less about levels of pay and more about how sensitive it is to what actually happens to the company. He cites one study that shows investing in companies where chief executives own lots of stock, and shorting those where they do not, earns between 4 and 10 per cent a year.

4) Reinforce the remuneration committee. As chair of the Barclays committee, Dame Alison Carnwath opposed a 2011 bonus for chief executive Bob Diamond. She was overruled and had to defend it at the bank’s annual meeting. Investors are now heaping pressure on Dame Ann Dowling, who heads the committee at BP. Her discomfort at the 59 per cent vote against Mr Dudley’s pay rise was plain. Compensation committees need to stand firm against chief executives and chairs. Where an extreme pay plan is out of tune with what the company achieved, directors need to use their discretion to cancel bonuses not yet paid, or claw back those already issued.

The BP revolt overshadowed the story earlier this month of Richard Pennycook, who has led Co-operative Group’s turnround and insisted on taking a 60 per cent cut in his base pay. It “reflects the type of organisation we are”, Allan Leighton, the mutual’s chairman, said. More companies should think what sort of values are reflected in their pay policies — and what impact those policies have on their fragile public licence to operate.

One last point. Do not try these remedies out on Ronaldo, unless you want to lose him to a rival. The implicit threat that a sought-after executive may leave often cows boards into agreeing extravagant pay deals. It should not. Directors overstate such risks by roughly the same amount that they overrate the talents of limelight-hogging chief executives.