  Context: Redshifts are fundamental for our understanding of extragalactic
X-ray sources. Ambiguous counterpart associations, expensive optical
spectroscopy and/or multimission multiwavelength coverage to resolve
degeneracies make estimation often difficult in practice.
  Aims: We attempt to constrain redshifts of obscured Active Galactic Nuclei
(AGN) using only low-resolution X-ray spectra.
  Methods: Our XZ method fits AGN X-ray spectra with a moderately complex
spectral model incorporating a corona, torus obscurer and warm mirror. Using
the Bayesian X-ray Astronomy (BXA) package, we constrain redshift, column
density, photon index and luminosity simultaneously. The redshift information
primarily comes from absorption edges in Compton-thin AGN, and from the Fe
K$\alpha$ fluorescent line in heavily obscured AGN. A new generic background
fitting method allows us to extract more information from limited numbers of
source counts.
  Results: We derive redshift constraints for 74/321 hard-band detected sources
in the Chandra deep field South. Comparing with spectroscopic redshifts, we
find an outlier fraction of 8%, indicating that our model assumptions are
valid. For three Chandra deep fields, we release our XZ redshift estimates.
  Conclusions: The independent XZ estimate is easy to apply and effective for a
large fraction of obscured AGN in todays deep surveys without the need for any
additional data. Comparing to different redshift estimation methods, XZ can
resolve degeneracies in photometric redshifts, help to detect potential
association problems and confirm uncertain single-line spectroscopic redshifts.
With high spectral resolution and large collecting area, this technique will be
highly effective for Athena/WFI observations.
