Previous research has shown that older adults performed worse in web search tasks, and attributed poorer performance to a decline in their cognitive abilities. We conducted a study involving younger and older adults to compare their web search behavior and performance in ill- defined and well-defined information tasks using a health information website. In ill-defined tasks, only a general description about information needs was given, while in well-defined tasks, information needs as well as the specific target information were given. We found that older adults performed worse than younger adults in well-defined tasks, but the reverse was true in ill-defined tasks. Older adults compensated for their lower cognitive abilities by adopting a top-down knowledge-driven strategy to achieve the same level of performance in the ill-defined tasks. Indeed, path analysis showed that cognitive abilities, health literacy, and knowledge influenced search strategies adopted by older and younger adults. Design implications are also discussed.