  We show that the analytic continuations of Helson zeta functions $ \zeta_\chi
(s)= \sum_1^{\infty}\chi(n)n^{-s} $ can have essentially arbitrary poles and
zeroes in the strip $ 21/40 < \Re s < 1 $ (unconditionally), and in the whole
critical strip $ 1/2 < \Re s <1 $ under Riemann Hypothesis.
