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Median pay for chief executives of the biggest U.S. companies slipped 4.6% last year, but the link between annual compensation and shareholder returns remained weak.

Shareholders like their corporate boards stocked with independent directors—men and women unencumbered by close ties to the company or its executives.

Buried deep in American companies’ securities filings is an indicator for how aggressively they are working to shield their income from the Internal Revenue Service and other tax authorities.