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 (API 579). 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 FFS evaluations. This paper will provide a comprehensive summary of deficiencies and concerns with current published methods for evaluating susceptibility of pressure equipment to potential brittle fracture failures. Additionally, the paper will provide an overview of the methodology employed in the recently proposed procedure modifications for Part 3 of API 579 to mitigate the current deficiencies.