Significant inconsistencies and inadequacies exist in the current brittle fracture screening procedures in the 2016 edition of API 579-1/ASME FFS-1, Fitness-For-Service. Results from an evaluation completed using the current published guidance could prove unsafe in some instances. The ASME/API Joint Committee on Fitness-For-Service (FFS) recently initiated a project to rewrite API 579 Part 3, Assessment of Existing Equipment for Brittle Fracture. The intent of the project is to establish new Level 1 and Level 2 evaluation procedures and acceptance criteria developed using state-of-the-art fracture mechanics consistent with the Part 9 Failure Assessment Diagram (FAD) approach, currently employed in Level 3 Fitness-For-Service evaluations. This presentation will provide a comprehensive summary of deficiencies and corresponding concerns with current published methods for evaluating susceptibility of pressure equipment to potential brittle fracture failures. The presentation will include a case study demonstrating the benefits of using detailed fracture mechanics and, lastly, the presentation will provide a brief introduction to the methodology employed in the recently proposed procedure modifications for Part 3 of API 579.