Gravitationally bound companions to stars enable determinations of their masses, and offer clues to their formation, evolution and dynamical histories. So motivated, we have carried out a speckle imaging survey of eight of the nearest and brightest Wolf-Rayet (WR) stars to directly measure the frequency of their resolvable companions, and to search for much fainter companions than hitherto possible. We found one new, close companion to each of WR 113, WR 115 and WR 120 in the separation range 0.2 - 1.2. Our results provide more evidence that similar-brightness, close companions to WR stars are common. More remarkably, they also demonstrate that the predicted, but much fainter and thus elusive companions to WR stars are now within reach of modern speckle cameras on 8m class telescopes by finding the first example. The new companion to WR 113 is just 1.16 distant from it, and is 8 magnitudes fainter than the WR star. The empirical probability of a chance line-of-sight of the faint companion at the position of WR 113 is < 0.5%, though we cannot yet prove or disprove if the two stars are gravitationally bound. If these three new detections are physical companions we suggest, based on their narrowband magnitudes, colors, reddenings and GAIA distances that the companions to WR113, WR 115 and WR 120 are an F-type dwarf, an early B-type dwarf, and a WNE-type WR star, respectively.