We present measurements of Josephson junctions containing three magnetic layers with noncollinear magnetizations. The junctions are of the form S/F'/N/F/N/F ''/S, where S is superconducting Nb, F' is either a thin Ni or Permalloy layer with in-plane magnetization, N is the normal metal Cu, F is a synthetic antiferromagnet with magnetization perpendicular to the plane, composed of Pd/Co multilayers on either side of a thin Ru spacer, and F '' is a thin Ni layer with in-plane magnetization. The supercurrent in these junctions decays more slowly as a function of the F-layer thickness than for similar spin-singlet junctions not containing the F' and F '' layers. The slower decay is the prime signature that the supercurrent in the central part of these junctions is carried by spin-triplet pairs. The junctions containing F' = Permalloy are suitable for future experiments where either the amplitude of the critical current or the ground-state phase difference across the junction is controlled by changing the relative orientations of the magnetizations of the F' and F '' layers.