  Context: Studies of the production and escape of Lyman Continuum from
galaxies often rely on array of indirect observational tracers in preselection
of candidate leakers.
  Aims: Here, we investigate how much ionizing radiation might be missed due to
these selection criteria by completely removing them and performing a search
selected purely from rest-frame LyC emission; and how that affects our
estimates of the ionizing background.
  Methods: We invert the conventional method and perform a bottom-up search for
Lyman-continuum leaking galaxies at redshifts $2 < z < 3.5$. Using archival
data from HST and VLT/MUSE, we run source finding software on UV-filter HST
images from the HUDF, and subject all detected sources to a series of tests to
eliminate those that are inconsistent with being ionizing sources.
  Results: We find 6 new and one previously identified candidate leakers with
absolute escape fractions ranging from 36% to 100%. Our filtering criteria
eliminate one object previously reported as a candidate ionizing emitter in the
literature, while we report non-detection in the rest frame Lyman continuum of
two other previously reported sources. We find that our candidates make a
contribution to the metagalactic ionizing field of $\log_{10}(\epsilon_{\nu}) =
25.32(+0.25)(-0.21)$ and $25.29(+0.27)(-0.22)$ erg/s/Hz/cMpc$^3$ for the full
set of candidates and for the 4 strongest candidates only; both values are
higher than but consistent with other recent figures in the literature.
  Conclusions: Our findings suggest that galaxies that do not meet the usual
selection criteria may make a non-negligible contribution to the cosmic
ionizing field. We recommend that similar searches be carried out on a larger
scale in well-studied fields with both UV and large ancillary data coverage,
for example in the full set of CANDELS fields.
