"Improve" of course is subjective. We deal with Tropical American woods and there are two that are very similar.
Spanish Cedar, which a lot of luthiers now use for necks, is called "Cedar" because of it's smell, but it's not a Cedar - it's the same genus as Mahogany with a similar appearance. It is a bit less dense, and the sound is warmer. It is the traditional wood for the soundbox of a Cuatro Venezolano and a lot of Mexican instruments as well. You'll see it referred to as "Cedro".
Royal Mahogany, Andiroba, or "Caobilla" in Spanish, is also in the same genus as Mahogany. You'll notice a difference in working it, but in appearance the Central American variety can be practically indistinguishable. Where it comes from determines the sound - the Central American species are softer than Mahogany - they are a cross between Caoba (Honduran Mahogany) and Cedro in sound. The South American species are not as pretty, but are a bit denser with a bit crisper sound.
Both Caoba and Cedro are restricted under CITES. Caobilla (Spanish signifying "little cousin of Caoba") is not.