What are some good Trojan War books that depict the entire span of the war?

The Iliad is obviously the most famous Trojan War book, but it takes place entirely within the 9th year of the 10 year war. What books start around the judgment of Paris and end around the sacking of Troy?

Are there any such books that are nearly as old as the Iliad?

I'm not looking for a reimagining, but just a straight telling of the myth.