We report Hall effect and resistivity measurements in InSe under pressure. The electron concentration strongly decreases under pressure in samples exhibiting 3D transport behaviour. This is explained by the existence of an excited minimum in the conduction band moving to lower energies under pressure. The related impurity level traps electrons as it reaches the band gap and approaches the Fermi level. In samples exhibiting 2D behaviour the electron concentration remains constant. This behaviour, together with the pressure dependence of the Hall mobility, is consistent with a previous model which considers high mobility 3D electrons and low mobility 2D electrons to contribute to charge transport along the layers.