Resistivity and photoconductivity measurements have been made, using hydrostatic pressures up to 75 kb on localised states in some III - V semiconductors, including ones with transition metal ions present. The systems investigated were GaAs: Sn, GaAs: Cr: S, n - In[x] G[1-x] As[y] P[1-y], InP: Fe and GaAs: Cr. Many electronic transitions involving localised states (some deep in the band gap) appear to have anomolously high pressure coefficients. Possible explanations are discussed.