The whole minimalist movement, if judged by designs, seems focused on the thickness of the shoe, as well as the heel to toe drop. In my experiences, a more important consideration is the durometer or hardness of the mid-sole construction.
When we run on a soft mid-sole, the shoe will tend to give way to our foot movements, which leads to destabilization of the weighted leg/foot. As we know, the running shoe industry confronts this with wedges and posts in the mid-sole. It seems a more ideal construction would be a shoe with a hard mid-sole, yet still thin and a highly flexible forefoot.
Many of the shoes that pass as minimalist have a thin mid-sole, but it is still soft enough to introduce distortions in the landing. I see this in other people and have felt it in my own running (and seen in the wear patterns of the out sole). Can anyone recommend or point to discussions of shoes that are still thin, yet very firm in mid-sole yet flexible in forefoot. And, have a very low heel to toe drop. One shoe I noted is the Adidas Fluid Tech. It's really more of a soccer trainer, but has the firm mid-sole (from from arch to heel) yet very flexible forefoot. It does not have, however, a thin mid-sole and there is a heel to toe drop.