For one thing, the United States broadcasts no television to much of the non-Arab Islamic world, relying on radio broadcasts by the Voice of America.

And, even though Sawa and Alhurra are gaining audiences in the Arab world, they are far outdistanced by Al Jazeera and Al Arabiya, which broadcast nonstop anti-U.S. propaganda, much of it almost pornographically drenched in blood and body parts.

The message, delivered with continual scenes of violence, is that the United States wants to control Middle East oil, wants to humiliate Muslims and is conducting a “crusade” against Islam.

When I asked Hughes whether she thought the United States was losing the ideological war, she said, “I’m an optimistic person. I think we have a long way to go. We have a lot more to do.”

Hughes commissioned a huge, 18,000-person poll in 14 countries, which showed high rates of disapproval of the United States — but a willingness almost everywhere to change their mind if the United States showed respect for their views and values and partnered with them in solving joint problems. Respect for other countries was not a hallmark of Bush’s first term. It is becoming more so in the second, thanks in no small part to Rice and Hughes.

Morton Kondracke is executive editor of Roll Call, the newspaper of Capitol Hill.