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We present a method for producing pairing-friendly, simple, ordinary Jacobian varieties of genus 2 hyperelliptic curves defined over a prime field . The proposed method heavily relies on the construction of a suitable p-Weil number and a corresponding quartic CM-field. Our Jacobians are absolutely simple and for this special class of Jacobians we give the first examples in the literature with -values below 4, while previous results had in general -values between 6 and 8. These examples derive from “families” of pairing-friendly Jacobians, which are basically polynomial representations of the Jacobian parameters.