Gauge origin independent calculations of nuclear magnetic shielding tensors are carried out inside the formalism of the continuous transformation of the origin of the current density leading to formal annihilation of its diamagnetic contribution (CTOCD-DZ). We employ the unrelaxed linear response approach with a hierarchy of different coupled cluster methods in order to assess the importance of the level of approximation in the coupled cluster expansion. The basis set dependence of the computed nuclear magnetic shielding constants is also analyzed in the series of correlation consistent basis sets, with the aim of designing optimized basis sets of relatively small size.