Purposeful carbon sequestration by direct injection into the deep ocean can store carbon for centuries. Even after injected carbon begins to leak back out to the atmosphere, much of the injected carbon will remain sequestered because of the acid neutralizing capacity of seawater. The slow leakage that occurs centuries into the future can give a false sense of security that the carbon and climate problem is under control. If this were to cause policy makers to become less vigilant about reducing the total emissions of anthropogenic carbon, our descendants would be penalized with having much higher carbon dioxide content in the atmosphere when leakage begins. This "carelessness feedback" would apply to other forms of sequestration that are not permanent. To avoid falling into this trap requires generations of policy makers to be aware of the feedback and committed to intergenerational equity.