Worcester's MP has called on the city council to allow people to park for free on Sundays in a bid to give businesses more trade.
Mike Foster said some small firms were closing down, partly due to large rent hikes and the loss of customers during the refurbishment of the High Street.
Simon Geraghty, deputy leader of the council, said free parking did not fit in with encouraging public transport.
But he added that discounts on Sundays might be considered in the future.
'Building site'
A one-day promotion encouraging more Sunday shopping is planned for October when parking could be half-price.
Mr Geraghty told BBC News: "Once we've tested the market, if we get enough business, we may look at a discount scheme.
"We are working with the Retailers' Forum to boost Sunday trading.
"But we've won money from the government on the back of promoting sustainable travel, i.e. more public transport, so free parking is a strategy that doesn't fit with that."
Mr Foster said people should be allowed to park for nothing as an incentive.
"Neighbouring towns have free parking on Sundays," he said.
"The High Street refurbishment took longer than expected. It was like a building site and the feeling is some customers went elsewhere for their shopping and haven't returned."