WASHINGTON  The Supreme Court on Thursday significantly narrowed the scope of a law often used by federal prosecutors in corruption cases and called into question the fraud convictions of Jeffrey K. Skilling, a former chief executive of Enron, and Conrad M. Black, a newspaper executive convicted of defrauding his media company.

The justices were unanimous in calling a broad interpretation of the law, which makes it a crime “to deprive another of the intangible right of honest services,” unconstitutionally vague.

The decision will have implications for many other cases, including those of former Gov. Rod R. Blagojevich of Illinois, who is on trial on charges of violating the law in Chicago, and Joseph L. Bruno, a prominent former New York politician, who was recently convicted of violating the law.

Many lower court judges and scholars have called the law hopelessly vague, saying it could apply to conduct as routine as calling in sick to go to a baseball game. The vagueness of the law, these critics said, gives potential defendants insufficient notice of what is a crime and prosecutors too much discretion in deciding whom to charge.