The conditions for the optimal operation of the pulsed nuclear-spin refrigerator are investigated in three crystals: Dy:YES, Yb:YES and Yb:YCl 3·6H 2O. The experiments were performed in the temperature range 0.1 ≲ T ⩽ 1 K, with static magnetic field values 0.5 ≲ H dc ≲ 10 kOe and a pulsed field H p ≲ 2 kOe, while the pulsed-field decay rate at cross relaxation, (d H p/d t) cr, had a maximum of 50 kOe/s. The magnetic-ion concentration was varied in the range 0.05 ≲ c ≲ 2%. Proton-spin temperatures were measured by continuous wave NMR. In the refrigeration process in all crystals, electron spin-spin interaction is found to play an important role, even at the lowest concentrations. In Dy:YES and Yb:YCl 3·6H 2O, in which g ⊥ is determined to be about 0.08, the production of nuclear polarization through proton-electron spin flips is speeded up by spin-spin interaction, in the absence of which cross-relaxation transitions would be very unlikely. Conversely, in Yb:YES, it is concluded in particular from the field dependence of the ratio of the maximum proton polarization and electron-spin polarization, that spin-spin interaction in this crystal forms an obstacle in the polarization method. This appears as a relatively large g 2 ⊥ value of 7 x 10 -5, compared with the squared proton g n value of 9 x 10 -6. Our results in Yb:YES indicate that proton polarizations of more than 70% could be realized. In view of the experiments of Potter and Stapleton it is suggested that an increase of (d H p/d t) cr by a factor 200, at low Yb concentrations c ⩽ 0.05%, will circumvent the problems of spin-spin interaction by reducing the apparent Yb spin g ⊥ value to g ⊥ ⩽ g n. The low concentrations then required, entail a polarization build-up and decay time of at least a few hours.