We tested a group of ten post-acute right-hemisphere damaged patients. Patients had no neglect according to paper-and-pencil cancellation tasks. They were administered computer-based single- and dual-tasks, requiring to orally name the position of appearance (e.g. left vs. right) of briefly-presented lateralized targets. Patients omitted a consistent number of contralesional targets (≈ 40%) under the single-task condition. When required to perform a concurrent task which recruited additional attentional resources (dual-tasks), patients' awareness for contralesional hemispace was severely affected, with less than one third of contralesional targets detected (≈ 70% of omissions). In contrast, performance for ipsilesional (right-sided) targets was close to ceiling, showing that the deficit unveiled by computer-based testing selectively affected the contralesional hemispace. We conclude that computer-based, attention-demanding tasks are strikingly more sensitive than cancellation tasks in detecting neglect, because they are relatively immune to compensatory strategies that are often deployed by post-acute patients.