Not inherently, no. However, these shoes aren't designed to be worn during strenuous workouts and so don't have as much support as more dedicated trainers like running shoes. There are high-top versions of Converse sneakers and these do provide slightly more ankle support, but they are still made of a lightweight canvas that can only do so much. If you've had problems with your ankles in the past but want to wear Converse while lifting, consider wearing proper ankle supports or straps to minimize the risk of further injury.