Pseudoneglect is the tendency for the general population to over-attend to the left. While pseudoneglect is classically demonstrated using line bisection, it also occurs for visual search. The current study explored the influence of eye movements and functional cerebral asymmetry on asymmetries for visual search. In Experiment 1, 24 participants carried out a conjunction search for a target within a rectangular array. A leftward advantage for detecting targets was observed when the eyes were free to move, but not when they were restricted by short exposure durations. In Experiment 2, the effect of functional cerebral asymmetry was explored by comparing 20 right-handers and 19 left-handers. Results showed a stronger leftward bias for the right-handers, consistent with a mechanism related to cerebral asymmetry. In Experiment 3, an eye-tracker directly controlled eye movements in 25 participants. A leftward advantage emerged when the eyes were still, but not when they were free to move. Experiments 1 and 3 produced contradictory results in relation to eye movements, which may be related to task-related demands. On balance, the data suggest that asymmetries in visual search can occur in the absence of eye movements and that they are related to right hemisphere specialisation for spatial attention.