  We study Cox rings of normal threefolds on which SL2 acts with a dense orbit.
Exploiting the method of U-invariants, we obtain combinatorial criteria for the
total coordinate space and the base variety to have log terminal singularities.
Then, we investigate the iteration of Cox rings and obtain a bound on its
length. Finally, we develop a general approach to the description of the Cox
ring by generators and relations which is effective for normal SL2
/$\mu$n-embeddings.
