Context. When studying the production and escape of Lyman continuum (LyC) from galaxies, it is standard to rely on an array of indirect observational tracers in the preselection of candidate leakers. Aims. In this work, 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 inverted the conventional method and performed a bottom-up search for LyC leaking galaxies at redshifts 2 ≲ z ≲ 3.5. Using archival data from HST and VLT/MUSE, we ran source finding software on UV-filter HST images from the Hubble Ultra Deep Field (HUDF), and subjected all detected sources to a series of tests to eliminate those that are inconsistent with being ionizing sources. Results. We find six 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, and we report non-detections 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 log10(ϵν) = 25.32−0.21+0.25 and 25.29−0.22+0.27 erg s−1 Hz−1 cMpc−3 for the full set of candidates and for the four 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.