  In previous works, we have demonstrated that the path integral for {\it real,
Lorentzian} four-geometries in Einstein gravity yields sensible results in
well-understood physical situations, but leads to uncontrolled fluctuations
when the "no boundary" condition proposed by Hartle and Hawking is imposed. In
order to circumvent our result, new definitions for the gravitational path
integral have been sought, involving specific choices for a class of {\it
complex} four-geometries to be included. In their latest proposal, Diaz
Dorronsoro {\it et al.}~\cite{DiazDorronsoro:2018wro} advocate integrating the
lapse over a complex circular contour enclosing the origin. In this note we
show that, like their earlier proposal, this leads to mathematical and physical
inconsistencies and thus cannot be regarded as a basis for quantum cosmology.
We also comment on Vilenkin and Yamada's recent modification of the "tunneling"
proposal, made in order to avoid the same problems. We show that it leads to
the breakdown of perturbation theory in a strong coupling regime.
