U.S. officials agree on two initial points. First, they don’t know exactly where he is, and if they did, they would attack his location either from the ground or air if they could.

Second, Baghdadi is practicing, in the words of one official, “extraordinary operational security” to keep his location secret.

For months, the general theory has been that he’s hiding in one of several buildings in or near the center of Raqqa. In fact, officials have described to CNN one potential target: a building that they believe at some point had a jail inside of it.

Officials also have long thought Baghdadi, like other ISIS leaders, chose the densely populated areas of central Raqqa as a hideout, believing the U.S. would not risk killing large numbers of civilians with an airstrike against him.