We investigate the possibility of using the ratio between the 2−10 keV flux and the [Ne V]3426 emission line flux (X/NeV) as a diagnostic diagram to discover heavily obscured, possibly Compton-thick active galactic nuclei (AGN) in the distant Universe. While it is on average about one order of magnitude fainter than the more commonly used [O III]5007 emission line, the [Ne V]3426 line can be observed with optical spectroscopy up to z ∼ 1.5, whereas the [O III]5007 line is redshifted out of the optical bands already at z ∼ 0.8. First, we calibrated a relation between X/NeV and the cold absorbing column density N H using a sample of 74 bright, nearby Seyferts with both X-ray and [Ne V] data available in the literature and for which the column density is determined unambiguously. . Based on the X/NeV ratio, complemented by X-ray spectral analysis, 2 objects appear good Compton-thick QSO candidates, 4 objects appear as Compton-thin QSOs, while 3 have an ambiguous classification. When excluding broad-lined QSOs with a red continuum from the sample and thus considering only genuine narrow-line objects, the efficiency in selecting Compton-thick QSOs through the [Ne V] line is about 50% (with large errors, though), more similar to what is achieved with [O III] selection. We discuss the possibility of applying the X/NeV diagnostic to deep X-ray surveys to search for Compton-thick Seyferts at z ∼ 1, i.e., those objects that are thought to be responsible for the "missing" X-ray background. Finally, we compared the optical spectral properties of [Ne V]-selected QSOs with those of other SDSS populations of obscured and unobscured QSOs. By restricting the analysis to objects in the same redshift (and luminosity) range z = [0.4−1.5], we found evidence that, at any given [Ne V] luminosity, increasing obscuration is accompanied by increasing [O II]3727 emission. This correlation is interpreted as evidence of enhanced star formation in obscured QSOs, which is consistent with current popular scenarios of BH-galaxy coevolution.