Color–magnitude diagrams (CMDs) for candidate companions in this survey. For each candidate we plot the absolute magnitude if the object were at the distance of the host star against the H2–H3 color. Black points indicate the expected trend for late-type stars: objects of spectral type T0 or later start to have significant methane absorption, and a correspondingly negative H2–H3 color. Faint candidates with H2–H3 ∼ 0 are inconsistent with being at the distance of the host star, and are therefore presumed to be background objects rather than co-moving companions. Specifically, we assume all candidates with M_H2 > 15 and H2–H3 > (15-M_H2)/1.5 are background objects. Those candidates without common proper motion data, for which the color–magnitude analysis is particularly important, are indicated with triangular points. The three large stars indicate the location of the three co-moving companions on the CMD, which are discussed further in Sections 6.1 to 6.3.