  Horava gravity has been constructed so as to exhibit anisotropic scaling in
the ultraviolet, as this renders the theory power-counting renormalizable.
However, when coupled to matter, the theory has been shown to suffer from
quadratic divergences. A way to cure these divergences is to add terms with
both time and space derivatives. We consider this extended version of the
theory in detail. We perform a perturbative analysis that includes all modes,
determine the propagators and discuss how including mixed-derivative terms
affects them. We also consider the Lifshitz scalar with mixed-derivative terms
as a toy model for power counting arguments and discuss the influence of such
terms on renormalizability.
