This paper states the problem of imprecision in the assessment of personal probabilities of those uncertain events that are here called "non-stochastic", since each event is not now reasonably considered to be a possible outcome of a well-defined stochastic process. It analyzes critically six previous attempts to solve the problem. Then it presents and defends a new solution based upon the standard concepts of personalistic Bayesian decision theory- The solution requires the decision maker to construct his Bayesian ">metamodel of his uncertain future assessments of the parameters (probabilities, and also utilities) in his decision model. He does this by assessing now his marginal personal probability distribution of each uncertain future assessment in a precise, coherent, and honest manner. It is proved that the expectation of each random variable is the precise, coherent, and honest assessment of the corresponding parameter. Analysis shows that this solution does not use second-order probability to represent imprecision in assessment.