Considerable attention has been devoted to understanding how objects are localized when there is ample time and attention to detect them. However, in the real world, we often must react to, or act upon, objects that we have glimpsed only briefly and are not directly at the focus of our attention. This paper describes two experiments examining the role of attentional constraints on 2-D (directional) localization, particularly in cases in which targets have been detected but are not within the spatial focus of attention. Targets were asterisks presented briefly (34-150 ms) above or below a central fixation point. Just prior to the target's appearance, a cue directed attention toward, or away from, the target. Participants indicated whether or not they saw the target, and then used a mouse to indicate the target's location. The impact of guessing was mitigated by removing trials that participants had flagged as not detected. Longer glimpses generally benefitted localization; by contrast, cue validity had very little effect on response sensitivity, bias or precision. At very brief durations, invalid cueing did result in a small increase in foveal bias. These results indicate that the directional location of objects can be extracted reasonably well from brief glimpses even with reduced attention. This directional information provides an important basis for 3-D localization of objects on the ground, via their angular declination. The current studies suggest that egocentric distance perception might be similarly robust to reduced attention when localization is based primarily on a target's angular declination.