CLEAN stripes are, in part, introduced by the approximations made during the minor cycles of a Clark CLEAN - they are less common when using a Högbom algorithm. Thus striping problems can be alleviated by taming the minor cycle approximations. There are two simple ways to tame the approximations used in the minor cycle of a Clark CLEAN - use a larger beam patch, and relax the criteria to perform a major cycle (i.e. perform fewer minor cycles per major cycle).
Cornwell (1983) (A&A 121, 281) suggested that the CLEAN stripe instability can be suppressed by the addition of a delta function to the dirty beam. For obvious reasons, this is popularly termed the `Prussian helmet' CLEAN. The spike is usually set at about 0.3. Together with this, one usually makes the loop gain smaller, to perhaps 0.05 or even 0.01. However, recent wisdom suggests that in general, the Prussian helmet is probably a red herring.