The piezoelectric constants of aluminum nitride and zinc oxide wurtzite-type nanowires have been calculated by first-principles approach and compared with the data obtained for bulk structures. The methods adopted here include the Hartree-Fock and density functional theory procedures in their periodic formulation. The piezoelectric response is seen to be higher in nanowires than in bulk. In zinc oxide wires, it is found that the piezoelectric constant is significantly enhanced by partial substitution of zinc by mercury.