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human
[Star Wars] Why didn't Vader kill Admiral Piett?

Was the revelation to Luke far too upsetting to him, or did he have ah int it wasn't Piett's fault and that executing him would not have helped?
gpt
He killed Ozzel because he was an arrogant priss who thought he knew better than Vader. He screwed up a large military operation with his own pride.

He killed Needa because he had the Falcon dead to rights and lost it off his scope. Instead of continuing the search, he gave up. Vader probably knew the ship couldn't have gotten far and was pissed Needa came grovelling instead of keeping up the chase.

Piett wasn't arrogant and didn't show weakness. He was a good commander and didn't flinch even in the face of failure and retribution. Vader recognized that and combined with his own internal turmoil decided it wasn't worth it to kill him.