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Mississippi enacted the law 2010. Other states and Congress have since enacted similar laws.
Backers of the laws say caller ID "spoofing" is a growing threat to people because of new technology making it cheap and easy to change the name and number that phone call recipients see on caller ID.
A spoofing service provider, TelTech Systems, challenged the Mississippi law in 2010. A federal judge in Mississippi sided with the company a year later.
The 5th U.S. Circuit Court of Appeals affirmed the ruling this week.