I invested in one of those antistatic brush arms, and that worked. Sort-of. It does have a tendency to swing into the middle track of the record and stay there, leaving the inner tracks unswept. This can hardly be considered thorough.
How much handier would it be to have something that actually tracked the stylus position and swept up any dust and fluff before it lands? Quite a lot handier, I think.
(Honesty time: I have vague memories of audiophile relatives having something similar in padded velvet, back when vinyl was King, but I haven't been able to find such a thing these days. So I made my own. Someone else invented this, though. Someone truly smart...)
Step 1: Gather the Bits.
* a scrap of soft material such as velvet or fleece (mine's left over from my son's turtle hat - excellent instructable, that...) to form the brush.
* The end of the ink reservoir from a Bic-style biro
* A twist-tie or length of fine wire (roughly 8-9 cm)
* Some glue
* A small lump of Sugru (less than a sachet; have something lined up to use up the rest of it. Fix that dodgy USB cable or something...)
Okay, blu-tack would probably work as well as Sugru, initially at least, but I like Sugru's permanence and lightness and all-round cool cred. So there.