As is well known, Scopus and WoS, unlike many other bibliographic databases, offer very precise filtering functions. It may happen that a peer-reviewer asks to broaden the search to prove that there are no "relevant" publications in other databases. But, if you are researching a familiar field, you know that the interested research community is already structured around the most relevant publications (in terms of citations). Refining results from other databases such as ERIC, CiteSeerX, IEEE explore etc. can be very time consuming. How do you justify the final decision for a particular database over others?
Are you doing bibliometric research where the search results from a given databased are used as data? If not, then the strategy you mentioned where the "interested research community is already structured around the most relevant publications" should be enough.
David L Morgan Yes, I am doing bibliometric research and then use database results to visualise bibliometric networks.
In that case, the only answer I can think of is subjective: You need to consider what collection of sources would be convincing to your audience. In my case I work with general rather than discipline-specific questions, so I either use WoS alone, or I combine WoS with Scopus and then eliminate duplicates.