  We give several new examples of computable structures of high Scott rank. For
earlier known computable structures of Scott rank $\omega_1^{CK}$, the
computable infinitary theory is $\aleph_0$-categorical. Millar and Sacks asked
whether this was always the case. We answer this question by constructing an
example whose computable infinitary theory has non-isomorphic countable models.
  The standard known computable structures of Scott rank $\omega_1^{CK}+1$ have
infinite indiscernible sequences. We give two constructions with no
indiscernible ordered triple.
