  Next-generation spectro-polarimetric broadband surveys will probe cosmic
magnetic fields in unprecedented detail, using the magneto-optical effect known
as Faraday rotation. However, non-parametric methods such as RMCLEAN can
introduce non-observable linearly polarized flux into a fitted model at
negative wavelengths squared. This leads to Faraday rotation structures that
are consistent with the observed data, but would be impossible or difficult to
measure. We construct a convex non-parametric $QU$-fitting algorithm to
constrain the flux at negative wavelengths squared to be zero. This allows the
algorithm to recover structures that are limited in complexity to the
observable region in wavelength squared. We verify this approach on simulated
broadband data sets where we show that it has a lower root mean square error
and that it can change the scientific conclusions for real observations. We
advise using this prior in next-generation broadband surveys that aim to
uncover complex Faraday depth structures. We provide a public Python
implementation of the algorithm at
\url{https://github.com/Luke-Pratley/Faraday-Dreams}.
