You can see how I taper on the end of the halyard
on the picture above too. I tape it together while working, removing the tape shortly before finishing the splice.
One of the very nice things to do with this, is what I was at here: a Flemish splice at the end of the halyard
to tie a messenger line too when you want to remove the halyard from the mast
(we do when we're not sailing for a while, so that there is no UV damage).
The trick of the Flemish splice is that it will pass clutches, blocks etc. because the diameter does not increase. You taper the core
(I used Vectran here but it's the same for Dyneema) and then just splice the outer braid on that tapered position. Here are two pics to show how I proceeded:
Easy and quick and you smile every time you make use of it