  Various holographic approaches to QCD in five dimensions are explored using
input both from the putative non-critical string theory as well as QCD. It is
argued that a gravity theory in five dimensions coupled to a dilaton and an
axion may capture the important qualitative features of pure QCD. A part of the
higher alpha' corrections are resummed into a dilaton potential. The potential
is shown to be in one-to-one correspondence with the exact beta-function of
QCD, and its knowledge determines the full structure of the vacuum solution.
The geometry near the UV boundary is that of AdS_5 with logarithmic corrections
reflecting the asymptotic freedom of QCD. We find that all relevant confining
backgrounds have an IR singularity of the "good" kind that allows unambiguous
spectrum computations. Near the singularity the 't Hooft coupling is driven to
infinity. Asymptotically linear glueball masses can also be achieved. The
classification of all confining asymptotics, the associated glueball spectra
and meson dynamics are addressed in a companion paper, ArXiv:0707.1349
