Hi Jeroen,
the slideUp and slideDown animations are happening at the same time,
because you're calling them one after another (and each takes a while
to complete).
One simple, yet not really elegant way of working around it is this:
Exclude the paragraph in the clicked element from the list of
paragraphs to be slid up by using not():
$('.accordion p:visible').not($(this).siblings('p')).slideUp('fast');
That way, even if the slideDown function set the paragraph to visible,
it will not be subject to the slideUp function.
Bernd