The ATC takes a secondary set of skills to lower someone [while belaying] from a long distance from above.” Both devices are capable of accommodating high-risk situations, but the GriGri is more likely to switch between uses at a faster rate, which can be essential in extreme or life-or-death situations.

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Daughter is using a Grigri as a self-belay device. This is expressly discouraged by Petzl, the manufacturer, on this page titled Self Belaying is Prohibited. That's pretty damning. As the page admits, some people do use a Grigri for self-belays, but it's not ideal and potentially dangerous.

GriGri & GriGri+ Differences One small addition is a steel plate on the right side where the rope runs while lowering. This will reduce the amount of wear over time and extend the life of the Grigri+ compared to the standard model. It also has an integrated "anti-panic" mode.