Safety-critical Cyber-physical Systems (CPS) in vehicles are becoming more and more complex and interconnected. There is a pressing need for holistic approaches for safety and security analysis to address the challenges. System-Theoretic Process Analysis (STPA) is a top-down safety hazard analysis method, based on systems theory especially aimed at such systems. In contrast to established approaches, hazards are treated as a control problem rather than a reliability problem. STPA-Sec extends this approach to also include security analysis. However, when we applied STPA-Sec to real world use cases for joint safety and security analysis, a Battery Management System for a hybrid vehicle, we observed several limitations of the security extension. We propose improvements to address these limitations for a combined safety and security analysis. Our improvements lead to a better identi cation of high level security scenarios. We evaluate the feasibility of the improved co-analysis method in a self-optimizing battery management system. We also discuss the general applicability of STPA-Sec to high level safety and security analysis and the relation to automotive cybersecurity standards.