Councillors have already agreed in principle to extend parking controls to Sundays – but will thrash out exactly how the change will be implemented at a meeting next week.
Options include bringing in full restrictions across all roads between 8.30am and 6.30pm, or limiting charges to the afternoon.
Another alternative would see restrictions limited to between 1pm and 6.30pm on everything except main roads, where charges would also operate in the morning.
The council’s own sums show the move could bring in as much as £595,000 a year in extra income.
But Sunday morning charges have been widely criticised by churches, who fear it could impact on congregations.
And in a consultation exercise, more than 80 per cent of residents opposed parking controls being introduced on Sundays and in the evenings.
Elsewhere, proposals also include providing more “shared use” parking spaces – available for both permit holders and paying motorists – as well as a roll-out of visitors’ permits.
Councillor Lesley Hinds, the city’s transport leader, said: “We’ve already agreed that we need to introduce some parking controls on Sundays, as the status quo is simply not sustainable now that Edinburgh, like so many other places, has become much more of a 24/7 city in terms of socialising and shopping habits.
“However, the committee required further information in order to make a decision on how parking could be controlled on Sundays and this report now sets out three different options.
“What we need to do is to achieve a balance between alleviating uncontrolled parking and increasing turnover for businesses and making travel easier for residents and visitors.
“It will be for the committee to decide, based on how the different options fit with consultation feedback and so on – once an option’s been agreed, we can finalise the Parking Action Plan and get ready to put it into action.”
Councillors will pick their preferred option for Sunday parking at a meeting of the transport and environment committee on June 7.
Cities that already charge drivers to park on a Sunday include Aberdeen, Dundee and Glasgow.