A graph superimposes the growth–decline curves of major Early Rider Empires, from 600 BCE to 600 CE. Compared to running messengers, the Achaemenid empire sharply boosted message speed by using horse relay stations. A major rise in empire area resulted, also helped by split delegation of provincial power. The Xiongnu steppe empire broke the Achaemenid size record hugely but briefly, while Han did so longer but minimally. Rome fell short in size but lasted longer. By population size Han mostly was top, but Maurya and Rome at times surpassed it. Most of these empires profited from religious tolerance, compared to previous theocracies; Sassanids were an exception. The Qin-Han rule established a harsh centralized bureaucracy, while Rome limited it, allowing for local autonomy. Han official contact with Hellenic Bactria in 127 BCE marks the first indirect linkage of states from the Pacific to the Atlantic.