I have been tasked with reducing the size of our database. I have extracted each blob, compressed it, and put it back in the database. The size of the database has not been reduced. From what I understand, the database will now use this un-allocated space for future record and blob additions. Is this correct?

From reading other posts, I could possibly zip the database, restore it and this will reduce the size by removing un-allocated space. Is there another method to reduce the database size after the blob data has been compressed?