  We discuss spherically symmetric black holes in the modified self-dual theory
of gravity recently studied by Krasnov, obtained adding a Weyl-curvature
dependent `cosmological term' to the Plebanski lagrangian for general
relativity. This type of modified gravity admits two different types of
singularities: one is a true singularity for the theory where the fundamental
fields of the theory, as well as the (auxiliary) spacetime metric, become
singular, and the other one is a milder "non-metric singularity" where the
metric description of the spacetime breaks down but the fundamental fields
themselves are regular. We first generalise this modified self-dual gravity to
include Maxwell's field and then study basic features of spherically symmetric,
charged black holes, with particular focus on whether these two types of
singularities are hidden or naked. We restrict our attention to minimal forms
of the modification, and find that the theory exhibits `screening' effects of
the electric charge (or `anti-screening', depending upon the sign of the
modification term), in the sense that it leads to the possibility of charging
the black hole more (or less) than it would be possible in general relativity
without exposing a naked singularity. We also find that for any (even
arbitrarily large) value of charge, true singularities of the theory appear to
be either achronal (non-timelike) covered by the hypersurface of a harmless
non-metric singularity, or simply hidden inside at least one Killing horizon.
