BY ALIZA APPELBAUM

Riverdale and Kingsbridge got a lucky parking break last month when street-cleaning rules were suspended for six to eight weeks. Now the rest of the Bronx will be getting even more good news when it comes to parking.

Four parking bills were discussed at the City Council meeting Monday afternoon that would give drivers some relief from the stringent enforcement of recent years. City Councilman Oliver Koppell has signed on to the bills as a sponsor.

The most-discussed bill would grant a five-minute amnesty period for cars with Muni-Meter receipts as well as those subjected to alternate side parking. Mayor Michael Bloomberg has threatened to veto the bill if it comes to a vote, saying Monday morning that it would cause “chaos” if everyone overstayed their parking throughout the city without repercussions.

“I think we have enough votes to override,” said Mr. Koppell.

Two bills that would affect Riverdale, Mr. Koppell said, would require notification of parking price increases or if parking is no longer allowed in a certain zone.

Parking meters in Riverdale changed recently from a quarter for a half hour to a quarter for 20 minutes of parking. Many Riverdalians were issued tickets because they were unaware of the change, Mr. Koppell said, adding that it would not happen again under the new law.

Monday’s fourth bill had to do with more lenient parking rules for clergy. Mr. Koppell said he expected all four bills to pass.

These bills are intended to give people those extra few minutes they need rather than feeling like they are being hounded by meter maids, Mr. Koppell said.

“It’s very frustrating to get a ticket after being one minute late,” he said.