Excessive IR-drop in capture mode during at-speed scan testing may cause timing errors for defect-free circuits, resulting in undue test yield loss. Previous solutions for achieving capture-power-safety adjust the switching activity around logic paths, especially long sensitized paths, in order to reduce the impact of IR-drop. However, those solutions ignore the impact of IR-drop on clock paths, namely test clock stretch; as a result, they cannot accurately achieve capture-power-safety. This paper proposes a novel scheme, called LP-CP-aware ATPG, for generating high-quality capture-power-safe at-speed scan test vectors by taking into consideration the switching activity around both logic and clock paths. This scheme features (1) LP-CP-aware path classification for characterizing long sensitized paths by considering the IR-drop impact on both logic and clock paths; (2) LP-CP-aware X-restoration for obtaining more effective X-bits by backtracing from both logic and clock paths; (3) LP-CP-aware X-filling for using different strategies according to the positions of X-bits in test cubes. Experimental results on large benchmark circuits demonstrate the advantages of LP-CP-aware ATPG, which can more accurately achieve capture-power-safety without significant test vector count inflation and test quality loss.