The title refers to the operatives of Burke's boss, ""The Man"". The Man has devised an ambitious project entitled Operation Eyeball. It is a plan to bug every foreign embassy in the world. Shortly before the plan is to be put into effect, a microfilm containing a list of American agents assigned to the operation is stolen, along with a photograph of each one. The list is being offered in trade for seven million in diamonds for international bidding on future targets. Even though the ransom is paid, The Man knows the list has been copied and so orders Burke and female agent Sylvia Kellogg to kill everyone connected with the theft. As they carry out the mission, Burke begins to suspect that Sylvia is working for the other side.

Sheik Farid, deposed King of Egypt, is collecting a secret aresenal of weapons to take over what he has lost. The Man assigns Burke to foil Farid's takeover plans. To help him, he has an elderly but effective British agent named Agatha Carruthers. Burke plans to romance Farid's mistress, Yasmin, and plant a bug in a fake diamond pendant he plans to give her.