Complex sentence: The U.S. and UK analysed the footage closely because they believed one of his body doubles may have been used, but the U.S. eventually said it believed the address was indeed delivered by Saddam Hussein himself.
Split into simpler sentences: The U.S. and U.K. analyze the footage closely, believing that one of his body doubles may have made the speech. However, the U.S. eventually says it believes the address was indeed delivered by Saddam Hussein himself.