The version on the ISA site is said to be more secure and is called 'a cow hitch with a better half'. The version in Jepson's book is simply 'a cow hitch with a half hitch'. Odd, because they are both drawn by the same illustrator.
Tie each version somewhat loosely and pull on the upper leg of the cow hitch just behind the bight. If you pull when the tail of the half hitch points in the same direction as when it went through the bight of the cow hitch (the TCC version), the hitch slips through the bight.
If you pull when the tail of the half hitch points in the opposite direction from when it went through the bight (the ISA version) the tail of the half hitch jams on the bight.
If the cow hitch is tied loosely with a 'better half' and you keep it loose with your hand you can continue to pull slack through the half hitch and the bight. But, when the hitch is in use the pull is on the other end of the sling--the eye where the block is hanging. This tightens the bight and prevents the half hitch from continuing to run. The danger with the TCC version is that the half hitch will slip through the bight when the load is first applied and the hitch initially tightens. If this happens then the whole hitch falls apart.
There is an article on the cow hitch and the girth hitch in an upcoming (maybe the next?) issue of Arborist News magazine.
Mahk