Opposite the Zeus Temple there are the remains of a small bouleuterion or odeon, but its history remains unknown.

A bouleuterion (Greek: βουλευτήριον) was a building which housed the council of citizens (boule) in Ancient Greece. There are several extant remains of bouleuteria around Greece and former Greek territories of ancient times. The ‘boule’, a basic institution of the ancient city-state (polis) in historical times, consisted of the citizens' representatives who assembled in order to confer and decide about public affairs. The word bouleuterion is composed from Greek boule (council) and the suffix -terion (place for doing something).

Odeon is the name for several ancient Greek and Roman buildings built for music: singing exercises, musical shows, poetry competitions, and the like. The word comes from the Ancient Greek ᾨδεῖον, Ōideion, literally "singing place", or "building for musical competitions"; from the verb ἀείδω, aeidō, "I sing".
In a general way its construction was similar to that of an ancient Greek or Roman theatre, but it was only a quarter of the size (or even less) and was provided with a roof for acoustic purposes, a characteristic difference.