The most common and most likely answer to this crossword clue is the 8 letter word MASSAGED
I've seen this crossword clue in The Sunday Telegraph
M
A
S
S
A
G
E
D
More clues leading to the result MASSAGED
Buddy explains!

The straight part
We know that "relieved tension, in a way" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case relieved tension, in a way = massaged.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does MASSAGED mean?
MASSAGED verb- To rub and knead (someone's body or a part of a body), to perform a massage on (somebody).
- To manipulate (data, a document etc.) to make it more presentable or more convenient to work with.
- To falsify (data or accounts).