Precise measurements of cross sections and complete sets of analyzing powers for the ( d, α ) reaction from 40Ca to the ground state 3 1 + and excited states 1 1 +, 1 2 +, 2 2 + of 38K at E d = 20 MeV have been analyzed in a finite-range distorted-wave Born approximation, using full sd-shell-model wave functions and including a D-state amplitude for the deuteron clusters in the α-particle. Deuteron tensor potentials were included and the influence of two-step processes estimated. The results are compatible with the previous determination of D 2 ( 4 He) = − 0.19 ± 0.04 fm 2 from the ground-state transition, which is found to be the most appropriate one for the determination of D-state effects.