  Continuing the study of complexity theory of Koepke's Ordinal Turing Machines
(OTMs) that was started by Rin, L\"owe and the author, we prove the following
results:
  (1) An analogue of Ladner's theorem for OTMs holds: That is, there are
languages $\mathcal{L}$ which are NP$^{\infty}$, but neither P$^{\infty}$ nor
NP$^{\infty}$-complete. This answers an open question of \cite{CLR}.
  (2) The speedup theorem for Turing machines, which allows us to bring down
the computation time and space usage of a Turing machine program down by an
aribtrary positive factor under relatively mild side conditions by expanding
the working alphabet does not hold for OTMs.
  (3) We show that, for $\alpha<\beta$ such that $\alpha$ is the halting time
of some OTM-program, there are decision problems that are OTM-decidable in time
bounded by $|w|^{\beta}\cdot\gamma$ for some $\gamma\in\text{On}$, but not in
time bounded by $|w|^{\alpha}\cdot\gamma$ for any $\gamma\in\text{On}$.
