The tools-common type db.DeferredQuery has a method EstimatedDocumentCount, but estimated counts are only possible on full collections, not on queries with filters.

As currently written, it will ignore the filter and return a full collection count, which is wrong.

I suggest the following changes:

• Run EstimatedDocumentCount on the underlying collection if the filter is nil or an empty BSON document
• Run CountDocuments on the underlying collection otherwise
• Consider renaming db.DeferredQuery.EstimatedDocumentCount to db.DeferredQuery.Count.