The new system will rely on a “self-releasing boot,” developed by the company PayLock, which secured a sole-source contract with the city last year.

Drivers who pay by phone are given a code to unlock the boot on site, the city said. They are then allotted 48 hours to return the boots to one of about a dozen locations in the city. Residents can also request that someone else come to remove the boot. If the city receives no contact from a car’s owner, the vehicle will be towed 48 hours after the boot is placed.

Officials said the change should drastically reduce the time that drivers have to wait before getting their vehicles back — and, often, the speed with which the city is paid.

But the shift seems to trade on a possible psychological tug: With a disabled car still in eyesight, and not banished to a faraway tow yard, will the lure of on-the-spot payment prove too powerful to ignore?

“I won’t say the language you might use, but you say, ‘What the hell happened to my car?’ ” David M. Frankel, the city’s finance commissioner, said of the towing system. “You can still be angry at the fact that you have to pay your parking tickets, but compared to getting it towed, it’s no comparison.”