The parasite cleanse needs to be done per directions in order to get all the buggers at all stages of their development. Otherwise you are just killing some, but leaving many more to just repopulate.
It is recommended to do the parasite cleanse first, as there can be parasites in the liver apparently, according to the info on curezone. However many folks do the Liver Flush before the parasite cleanse. I did because I was having problems with my liver. It was fine for me, however I could have, I would have followed the advice of the experienced folks on this board and done the parasite cleanse first.