  In this paper, we extend Jones' result -- that cons-free programming with
$k^{th}$-order data and a call-by-value strategy characterises EXP$^k$TIME --
to a more general setting, including pattern-matching and non-deterministic
choice. We show that the addition of non-determinism is unexpectedly powerful
in the higher-order setting. Nevertheless, we can obtain a non-deterministic
parallel to Jones' hierarchy result by appropriate restricting rule formation.
