We previously found a dominant eye perceptional advantage in feature search (Vision Research, 2006). We now ask if this advantage extends to difficult conjunction search, which requires focused attention and depends on different cortical hierarchy levels. We determined eye dominance by the Hole-in-the-Card test. Using red-green glasses, subjects viewed a briefly presented, backward-masked, array of red/green dotted squares and filled circles. On half of the trials a filled square target replaced one dotted square. There was significantly better performance when the target was seen by the dominant eye, suggesting its visual processing priority in slow, as in rapid search, perhaps including augmented attention to dominant eye representations. Binocular conjunction targets were found faster than monocular targets, though binocularity--as utrocular information--was insufficient to support reasonable detection levels.