Detection reaction time (RT) at an extrafoveal location can be increased by noninformative precues presented at that location or ipsilaterally to it. This cue-induced inhibition is called inhibition of return or ipsilateral inhibition. We measured detection RT to simple light targets at extrafoveal locations that could be designated for covert orienting by local or distant cues. We found that cue-induced inhibition co-occurred in an additive fashion with the direct effects of covert orienting, i.e., it detracted from facilitation at attended locations and increased the disadvantage for unattended locations. Thus, cue-induced inhibition cannot be suppressed by a volitional covert orienting to the cued location; the cooccurrence of different facilitatory and inhibitory effects confirms the simultaneous operation of multiple independent, attentional mechanisms during covert orienting.