Olga seemed simultaneously awestruck and wary as she ran her fingers across the envelope. The sender seemed to be important: the "Presidential Administration." Was it mail from the Kremlin? "But the envelope felt strange," says Olga, who is secretary to the editor-in-chief of the Russian newspaper Novaya Gazeta.

When she finally opened the envelope, she felt something cold and leathery inside: the severed ears of a donkey. "One needs strong nerves here," she says. Four of the newspaper's journalists have already been...