WASHINGTON — Since 1978, a secret court in Washington has approved national security eavesdropping on American soil — operations that for decades had been conducted based on presidential authority alone.

Now, in response to broad dissatisfaction with the hidden bureaucracy directing lethal drone strikes, there is an interest in applying the model of the Foreign Intelligence Surveillance Act court — created by Congress so that surveillance had to be justified to a federal judge — to the targeted killing of suspected terrorists, or at least of American suspects.

“We’ve gone from people scoffing at this to it becoming a fit subject for polite conversation,” said Robert M. Chesney, a law professor at the University of Texas. He said court approval for adding names to a counterterrorism kill list — at least for American citizens abroad — “is no longer beyond the realm of political possibility.”

A drone court would face constitutional, political and practical obstacles, and might well prove unworkable, according to several legal scholars and terrorism experts. But with the war in Afghanistan winding down, Al Qaeda fragmenting into hard-to-read offshoots and the 2001 terrorist attacks receding into the past, they said, it is time to consider how to forge a new, trustworthy and transparent system to govern lethal counterterrorism operations.