Councillor Judith Callaghan, the chairwoman of the tree task group, said topping the branches was a "stupid idea" which would make the situation worse.
"It's a stupid idea to top them, then they'll get twice as thick. Get someone in who is a proper arborist and can resolve [the residents' concerns]."
Mayor Gary Daniell reminded fellow councillors that the survey showed most residents wanted the trees removed.
Mrs Callaghan said the trees cast a huge shadow and posed a number of problems for residents, such as extensive leaf dropping, boundary encroachment and roots lifting lawns and footpaths. However, she said removing them would be a travesty.
"I don't think topping them will reduce the shadow," she said.
"They are the most beautiful trees. If we were to cut them down, we would be committing vandalism."
Mr Daniell then proposed that the trees should be thinned and lifted by an arborist, and all councillors backed his proposal.
Last month, the Masterton District Council parks and open spaces task group agreed on a course of action to reduce the canopies of the trees.
Grant Hathaway, parks and facilities manager of Masterton District Council, said the remedial work would take place before the end of June.