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Would a possibility of reincarnation not then remove the need for a Saviour?

The answer to this question is to say that without the atonement, progress of any kind becomes impossible.

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Do I need multiple life attempts to get it right or can the Saviour make up the difference of my short comings?

This life is the time for you to prepare to meet God. Every soul born on this Earth has the potential, in a single human lifetime, to achieve exaltation. It can be accomplished in a single lifetime, that is clear to me. I believe reincarnation is the exception, and not the rule. I do not know that for certain. It may be that everyone on this earth today has been here several times. It may be that less than 2% of the Earth's current population lived previous lives. The atonement can cover most sins. The sins of King David were not forgiven in his lifetime. He lost his exaltation, and the kingdom was divided. Is it possible he will be reincarnated and regain his exaltation?

We live in the Dispensation of the Fullness of Times. This dispensation precedes that of the End of Times. Our dispensation is that of the "Restoration" of all things as from the beginning. We have witnessed it with reference to polygamy, priesthood, temples . . . David's soul will not remain in hell. He will not remain a "ghost."