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Various holographic approaches to QCD in five dimensions are explored using input both from the putative five-dimensional 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 YM theory. A part of the effects of higher α'-corrections is resummed into a dilaton potential. The potential is shown to be in one-to-one correspondence with the exact β-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 …