The electrical resistivity rho of the iron-arsenide superconductor Ba1-xKxFe2As2 was measured in applied pressures up to 2.6 GPa for four underdoped samples, with x = 0.16, 0.18, 0.19 and 0.21. The antiferromagnetic ordering temperature T_N, detected
as a sharp anomaly in rho(T), decreases linearly with pressure. At pressures above around 1.0 GPa, a second sharp anomaly is detected at a lower temperature T_0, which rises with pressure. We attribute this second anomaly to the onset of a phase that causes a reconstruction of the Fermi surface. This new phase expands with increasing x and it competes with superconductivity. We discuss the possibility that a second spin-density wave orders at T_0, with a Q vector distinct from that of the spin-density wave that sets in at T_N.
