New World diseases?

What diseases did the New World provide to the Old?

We all know about syphilis. Were there other diseases? Surely the answer is yes.

A reddit-er notes that Europeans very often did get sick. "when we read the accounts of early Spanish entradas in the U.S. Southeast, the authors make specific mention of crew members becoming ill weeks after their arrival in new lands" Cocoliztli didn't spread to the Old World, but didn't come from there either. "Giardia, Entamoeba, and Cryptosporidium" and other parasites were common. "...Jamestown, where of the > 3,500 who arrived from 1617-1622, only 1,240 were alive in 1622. The chief cause of death was endemic illness, and the term "seasoning" was commonly used to describe the disease transition new immigrants needed to go through before their survival was more assured"

It sounds like there was plenty of disease, though if much beyond syphilis made the return trip it got lost in the noise of Old World / African diseases. If you can transport a sick person fast enough he could infect others at the far side, or if the disease was a recurring one (malaria), or if the vector could survive the trip (rats) you could transfer the disease across the ocean.

UPDATE: AVI points out that malaria was suspected. The model would be that within a group a few people had latent malaria, and when it resurfaced (that happened to me, BTW), if there were anophelese mosquitoes around the rest of the group could get it and spread it. Europe/England has species of this kind of mosquito, but apparently some of them are not efficient trasmitters. An "indoor" disease? But England certainly had malaria: "By the 14th century ague was usually referred to tertian or quartan fevers (fevers occurring every third or fourth day)"--vivax, ovale, or falciparum vs malariae for the every 4 days.

So I'd guess that either the "seasoning" referred to malaria+ (+ malnutrition, + some other bug, possibly intestinal), or it was actually something else. Yellow fever, maybe? But malaria was certainly part of the cocktail that destroyed so many Europeans visiting tropical rainforest Africa.