It was a dark and stormy night, and as the people of uk.rec.gardening
huddled around the fire, Stephen Howard told them this story:

I have four beds at the moment, with similarly heavy soil ( on my
third fork in less than six years! ) - and I've had crappy root veg up
'til last year.
What I did was dig out a 4x4 plot and fill it with very old well
rotted manure to a depth of a foot. I then used that for my carrots -
and I have to say they shot right down!
Better still, they pulled up dead easy.... as did the resulting weeds!

Gosh! What we tried was to dig out (to about a foot or so) something
about the size of 2'x2', sifted out all the stones (that's why it wasn`t
any bigger: we were exhausted after that), and filled up the space left
by the stones (about half the total volume) with a mixture of sand and
compost. And we still got virtually nothing. I have a feeling the
seeds all rotted, but several started growing before disappearing, so
maybe they all got eaten.

Rhiannon, picked out four carrots about the size and shape of small
marbles, so won`t be trying that again.