"You can't expect to shoot someone 3 times and claim self defense, not in California anyway. If you shoot more than once, you better have a convincing story."

You are correct in that you had better have a convincing story and hopefully direct evidence and physical evidence to justify your actions. I disagree that you are limited to shooting a person once if they are a lethal threat to you. You should shoot until the threat is no longer a threat whether it be the suspect gives up, runs away or is incapacitated.

The reason you took the action to shoot them in the first place is because you perceived that they were taking substantial action to kill you or gravely injure you. But California is one of those special places where certain people are attempting to outlaw self defense altogether. So you may be right. That's one of the reasons I don't live in California.

The minimum response should be two rounds or more to the center of mass and maybe a third to the head if the two did not do the job. This is the gory reality of armed conflict. People don't go down with one shot like on TV.
This is the stuff that one should prepare one's self for if they plan to be armed.

Regards,
Green and Tan