  The point-spread function (PSF) is a fundamental property of any astronomical
instrument. In interferometers, differing array configurations combined with
their $uv$ coverage, and various weighting schemes can produce an irregular but
deterministic PSF. As a result, the PSF is often deconvolved using CLEAN-style
algorithms to improve image fidelity. In this paper, we revisit a significant
effect that causes the flux densities measured with any interferometer to be
systematically offset from the true values. Using a suite of carefully
controlled simulations, we show that the systematic offset originates from a
mismatch in the units of the image produced by these CLEAN-style algorithms. We
illustrate that this systematic error can be significant, ranging from a few to
tens of per cent. Accounting for this effect is important for current and
future interferometric arrays, such as MeerKAT, LOFAR and the SKA, whose
core-dominated configuration naturally causes an irregular PSF. We show that
this offset is independent of other systematics, and can worsen due to some
factors such as the goodness of the fit to the PSF, the deconvolution depth,
and the signal-to-noise of the source. Finally, we present several methods that
can reduce this effect to just a few per cent.
