We study the problem of navigating through a database of similar objects using comparisons under heterogeneous demand, a problem closely related to small-world network design. We show that, under heterogeneous demand, the small-world network design problem is NP-hard. Given the above negative result, we propose a novel mechanism for small-world network design and provide an upper bound on its performance under heterogeneous demand. The above mechanism has a natural equivalent in the context of content search through comparisons, again under heterogeneous demand; we use this to establish both upper and lower bounds on content search through comparisons.