Fresh Web Explorer supports a ton of great search operators that will help you refine what you're looking for. Just pop them open from the "Show search operators" button under the search field.
If you're seeing a lot of unrelated mentions you can exclude irrelevant topics with the “–” operator.
You can also use operators to focus in on subjects with quotation marks, AND, and OR.
Find results for new links to the root domain of your competitor.
Find mentions of "Moz Pro" that don't link to the root domain moz.com.
Find whenever "keyword" is mentioned specifically on the domain moz.com.