Was The Destruction Of Alderaan Morally Just?

From what I understand the Rebels had killed quite a few innocent Imperials, just doing their jobs, whilst stealing the Death Star plans, etc.

The Evil Empire was no doubt aware that a number of these insurgents were based on Alderaan and probably hidden among the civilian population.

However, these insurgents had caused the deaths of many innocent lives. Therefore was the Evil Empire justified in blowing up every single man, woman and child on the planet to ensure the eradication of some of these rebel leaders?

Would the arguement that these children were innocent be flawed anyway, since they'd probably all grow up to be future rebel terrorists anyway?