A method called partial completion is proposed for predicting the gain in precision of the Kaplan-Meier survival curve associated with additional follow-up and accrual. This is accomplished by using the initial data to predict the numbers of patients who would be at risk at the observed death times by the end of the proposed second follow-up period. A consistency result ensures that the predictors will be accurate in large samples while simulation results suggest that the predictors are accurate with moderate sample sizes. The procedures are applied to a bone marrow transplant study and the Channing House data set.