This paper contributes to the classification of commutative rings having an abundance of Noetherian overrings. Gilmer and Mott have characterized the domains whose proper overrings are Noetherian. In unpublished work, Eakin has shown that adjoining all Noetherian domains to the catalogue of Gilmer-Mott gives a description of the domains whose simple proper overrings are Noetheri an. Using the theory of Krul rings and valuation rings with few zero-divisors, the present article extends the latter characterization to the context of reduced rings