A Jemdet Nasr cylinder seal (red limestone 1.5 cm) It's from the "seated women" or "pigtailed" group. Please see references from Tell Asmar and Tell Agrab. Other parallels come from Fara, ancient Shuruppak (see Moortgat 35-37), Uruk (see Moortgat 38-39) and Susa (see Susa 719-725)

This is an Early Dynastic seal (brown veined marble, 2.7 cm) the triangular heads being typical for that period.
Seals with double registers are especially common in the period EDIIIa c. 2600-2500 B.C., see the parallel from the royal tombs at Ur. Interestingly there is a seal in the Anavian collection with a similar detail in the lower register: A goat eating from a tree, see picture.

This is an Early Dynastic II-III cylinder seal (lapis, 2.4 cm) dated around 2500 B.C. It depicts a contest frieze, two lions attack two horned animals, flanked by a scorpion. Below the seal impression see a parallel seal in Moortgat 1940, achieved in Bagdad 1886/87. Interestingly it was made in the same technique: drilled layout and the final cut afterwards. The Lapis found in the Near East was imported from Afghanistan, ancient Bactria. Dr. Winkelmann (see links) thinks, that this seal was made in Iran.

Seal impressions