We report a study of the modes B± → DK ± and B± → DK± where D() decays to CP eigenstates. The data sample used contains 275 × 106 BB̄ events at the Y(4S) resonance collected by the Belle detector at the KEKB energy-asymmetric e+e- collider. The CP asymmetries obtained for DCPK are: script A sign1 = 0.06 ± 0.14(stat) ± 0.05(sys), script A sign2 = -0.12 ± 0.14(stat) ± 0.05(sys) and for DCPK: script A sign1 = -0.20 ± 0.22(stat) ± 0.04(sys), script A sign*2 = 0.13 ± 0.30(stat) ± 0.08(sys). © 2006 The American Physical Society.