  The QCD axion is the leading solution to the strong-CP problem, a dark matter
candidate, and a possible result of string theory compactifications. However,
for axions produced before inflation, symmetry-breaking scales of $f_a \gtrsim
10^{12}$ GeV (which are favored in string-theoretic axion models) are ruled out
by cosmological constraints unless both the axion misalignment angle $\theta_0$
and the inflationary Hubble scale $H_I$ are extremely fine-tuned. We show that
attempting to accommodate a high-$f_a$ axion in inflationary cosmology leads to
a fine-tuning problem that is worse than the strong-CP problem the axion was
originally invented to solve. We also show that this problem remains unresolved
by anthropic selection arguments commonly applied to the high-$f_a$ axion
scenario.
