A Cuban spy case that embodied lingering Cold War tensions between the United States and the island nation died in the U.S. Supreme Court on Monday.

The justices, without elaboration, chose not to hear the final appeal of the so-called Cuban Five. The Cuban men, whose appeal won support from 10 Nobel laureates, claimed they did not receive a fair trial because of the anti-Castro climate enveloping their 2001 proceeding in Miami.

The high court's decision means the five will not get a shot at a new trial and will continue to serve lengthy prison terms ranging from 15 years to life.

The five, arrested in 1998 as members of La Red Avispa (the Wasp Network), were convicted of acting as illegal agents for Cuban leader Fidel Castro's government. Three were also found guilty of espionage conspiracy.

The group's ringleader, Gerardo Hernández, also was convicted of conspiring to commit murder for his supporting role in the Cuban government's highly controversial shoot-down in 1996 of two Miami-based planes over international waters – killing four members of the Brothers to the Rescue exile group.

The high court's decision not to review the Cuban Five's case drew praise from victims' relatives and Miami politicians. But it also brought condemnation from the Cuban government and an advocacy group, the National Committee to Free the Cuban Five.

"This is the best news in a long time," said Maggie Khuly, a Miami architect whose brother, Armando Alejandre Jr., was killed in the shoot-down. "It's not everything that we might have wanted, but this measure of justice is what we have right now."

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