Rocha Fernandes Furniture, 2018-01-07 02:44:05. Firm mattresses. Firm mattresses fall in 3 categories: firm, extra-firm, ultra-firm. The firm mattresses include the Orbit, Neptune Cotton Only and the Single Foam futon mattresses. Usually, these firm mattresses have very little foam, and are cotton only, giving it the firm feeling. The ones with foam use a denser foam that makes the mattress less soft. These mattresses are great for people who like to sleep on something firm and who need the additional support. The extra-firm mattresses include the Simmons Monarch 2 and the Liberty Futon Mattress. Some of these mattresses are created with very dense layers of foam from top to bottom. Finally, the ultra-firm mattresses are for those that love to sleep on the ground. These mattresses are usually not recommended for a futon frame, but more for a platform bed. These are for people who want that firm feeling of a traditional Japanese futon mattress. The high density of the foam makes these mattresses very heavy and harder to move around.