A new effect of selective enhancement of auxeticity through the changes of nanochannels’ diameter in Yukawa systems is reported. Elastic properties of the model of Yukawa crystals with narrow nanochannels in the [001] crystallographic direction have been studied by Monte Carlo simulations in the isobaric–isothermal ensemble. It has been found that the choice of nanochannels’ diameter allows one to decrease the Poissons ratio value of the system in one of two selected crystallographic directions. The value of Poisson’s ratio in those directions can be changed in a wide range, e.g. from −0.061(9) to −0.625(44) in the -direction, depending on the nanochannels’ type and the Debye screening length.