In this paper, we analyze the nuclear polarization of the spin-polarized Dy6Fe23 used in our two equivalence principle (EP) experiments. From this we infer the equivalence of polarized Dy in the earth's gravitational field to be good to 10(-3) and in the solar field to be good to 1.4 x 10(-2). To increase the nuclear polarization in order to have better EP tests, we propose to use a dilution refrigerator to lower the temperature to 10 mK. We present a thorough analysis of our experimental scheme together with a discussion of perspectives.