Rev Christopher Brown told the BBC that complaints centred on the 8am peals at St Mary's Church.
He said: "We had a couple of grumbles about the 8am bells. People who live close to Fishguard Square endure a bit of noise on Saturday nights."
However, the bells haven't been completely silenced.
Residents will have to make do with hearing the bells at 10am for the later service.
Explaining why the church decided to compromise, Brown said: "We decided to go along with their requests as an act of good neighbourliness."
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