We present the results of a study for the design of a fast extraction kicker to be installed in the Accelerator Test Facility ring at KEK. This activity is carried on in the framework of the ATF2 project, which will be built on the KEK Tsukuba campus as an extension of the existing ATF, taking advantage of the world s smallest normalized emittance achieved there. ATF2's primary goal is to operate as a test facility and establish the hardware and beam handling technologies envisaged for the International Linear Collider. In particular, the fast extraction kicker object of the present paper is an important component of the ILC damping rings, since its rise and fall time define the minimum distance between bunches and ultimately the damping rings length itself. Building on the initial results presented at EPAC '06, we report on the present status of the kicker design and define the minimum characteristics for pulsers and other subsystems. In addition to the original scheme with multiple stripline modules producing a total deflection of 5 mrad, we also investigated a scheme with a single kicker module for a reduced deflection of 1 mrad placed inside a closed orbit bump, which takes the electron closer to the extraction septum.