  The information lost in images of undersampled CCD cameras can be recovered
with the technique of `dithering'. A number of subexposures is taken with
sub-pixel shifts in order to record structures on scales smaller than a pixel.
The standard method to combine such exposures, `Drizzle', averages after
reversing the displacements, including rotations and distortions. More
sophisticated methods are available to produce, e.g., Nyquist sampled
representations of band-limited inputs. While the combined images produced by
these methods can be of high quality, their use as input for forward-modelling
techniques in gravitational lensing is still not optimal, because the residual
artefacts still affect the modelling results in unpredictable ways. In this
paper we argue for an overall modelling approach that takes into account the
dithering and the lensing without the intermediate product of a combined image.
As one building block we introduce an alternative approach to combine dithered
images by direct model fitting with a least-squares approach including a
regularization constraint. We present tests with simulated and real data that
show the quality of the results. The additional effects of gravitational
lensing and the convolution with an instrumental point spread function can be
included in a natural way, avoiding the possible systematic errors of previous
procedures.
