The move against the fundraising exceptions for wealthy candidates is the latest blow to McCain-Feingold reforms.
The case involved a California man who killed his ex-girlfriend after she complained to police.
The ruling, a victory for Exxon, reduced the $2.5 billion punitive damages to about $500 million.
In a 5-to-4 ruling, the justices decide child rape isn't a capital offense.
They could help avoid judicial conflicts of interest.
At issue: Can a judge enforce environmental rules at the expense of national defense training?
In a ruling Thursday, it guides federal judges to weigh conflicts of interest by insurance companies.
Justices rule 7 to 2 that some defendants aren't competent enough to represent themselves.