From the LifeStraw FAQs:
Q: Does LifeStraw® personal remove parasites like cryptosporidium and giardia?
A: No, the present version does not filter any parasites. I've got a couple of the
Frontier Filter Straws in various kits as back-up. They claim down to 2 microns, and purportedly they grab crypto and giardia. I've not personally tested.
Edit: Found that McNett/Aquamira now has a slightly larger "big brother" to the Frontier Straw — the
Aquamira Frontier Pro. Attaches to tubes, bottles, etc. and has pre-filter. 1-1/4 in. x 5-1/2 in. Inexpensive.