The electrical resistivity ρ of the iron-arsenide superconductor Ba _1-xK _xFe ₂As ₂ was measured in applied pressures up to 2.6 GPa for four underdoped samples, with x0.16, 0.18, 0.19, and 0.21. The antiferromagnetic ordering temperature T _N, detected as a sharp anomaly in ρ(T), decreases linearly with pressure. At pressures above P1.0 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. The 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.