A dying character must first be stabilized before he or she can be truly healed. Unless stated otherwise, the first application of supernatural healing only stabilizes the condition of the wounded character (to zero hit points). The next application of healing can raise the character's hit points to a maximum of 1. From that point, the healing powers have their full, normal effect. In other words, it takes three healing invocations to make a difference.
For a critically injured character, this is the safest and most effective method of healing. As stated earlier, supernatural healing powers never leave scarring or infection.