Yes, precisely. What I didn't mention is that once we've established that it's being used, we then have to decide whether the marginal gain from having the narrower index is worth the cost of maintaining it. If the wider index is much wider, then it's possible the narrower index provides a significant performance advantage, or maybe a performance advantage on an important query. These are all questions whose answers can only be known from an understanding of the data, usage patterns and business requirements.
John