A compassionate heart still feels anger, greed, jealousy, and other such emotions. But it accepts them for what they are with equanimity, and cultivates the strength of mind to let them arise and pass without identifying with or acting upon them.
Compassion is not devoid of discernment and courage. Just as we need the courage to respond to the anguish of others, so we need the discernment to know our limitations and the ability to say "no." A compassionate life is one in which our resources are used to optimum effect. Just as we need to know when and how to give ourselves fully to a task, so we need to know when and how to stop and rest.— Stephen Batchelor in Buddhism Without Beliefs