  We describe a new multi-scale deconvolution algorithm that can also be used
in multi-frequency mode. The algorithm only affects the minor clean loop. In
single-frequency mode, the minor loop of our improved multi-scale algorithm is
over an order of magnitude faster than the CASA multi-scale algorithm, and
produces results of similar quality. For multi-frequency deconvolution, a
technique named joined-channel cleaning is used. In this mode, the minor loop
of our algorithm is 2-3 orders of magnitude faster than CASA MSMFS. We extend
the multi-scale mode with automated scale-dependent masking, which allows
structures to be cleaned below the noise. We describe a new scale-bias function
for use in multi-scale cleaning. We test a second deconvolution method that is
a variant of the MORESANE deconvolution technique, and uses a convex
optimisation technique with isotropic undecimated wavelets as dictionary. On
simple, well calibrated data the convex optimisation algorithm produces
visually more representative models. On complex or imperfect data, the convex
optimisation algorithm has stability issues.
