Reliability updating by inspections has become widely used in the offshore industry, especially within the framework of FORM/SORM. However, certain algorithmic difficulties can occur. This is especially true for reliability updating in the presence of structural fatigue (crack propagation and instability), but the problem appears to exist whenever conditional probabilities are to be calculated. New and widely successful strategies to select appropriate starting points for the β-point search as well as strategies to avoid physically or mathematically inadmissible domains are proposed. They are illustrated at a typical example in which it is also demonstrated that the simpler crude FORM approaches are inadequate.