The Supreme Court is allowing a bigger award of money to victims of the 1998 bombings by al-Qaida of the U.S. embassies in Nairobi, Kenya, and Dar es Salaam, Tanzania. Despite the court's ruling, however, the victims may only ever collect a fraction of the billions of dollars a lower court awarded.

The nearly simultaneous truck bombings at the embassies killed 224 people and injured thousands. They were the first major attacks on U.S. targets by al-Qaida.

The case the Supreme Court ruled in involves lawsuits filed by victims and their families against Sudan. The lawsuits accused the country of...