Crain’s New York reports that when a health-department inspector visited XES Lounge in Chelsea last month, he gave general manager Tony Juliano a ticket for having unwrapped straws on the bar. Those straws have been there for nearly eight years, but this time it was deemed a $400 violation.

A few months earlier, inspectors cited the business for a missing “No smoking” sign in the back of the bar, which has 11 employees. “We’ve been open since 2004 and were never cited for that,” said Mr. Juliano.

His frustrations echo that of many small business owners in the city, who view fines for minor offenses as punitive and feel the process for paying and contesting violations is burdensome.

In mid-October, Marisol Chino, the owner of Tepeyac Deli & Grocery on Irving Avenue in Brooklyn, was cited for having a metal food stand outside, instead of a wooden one. “They’ve been inspecting me for seven years and never told me that,” she said. “They gave me the option to pay a $200 fine or fight it, but if I lose, the fine goes to $1,000.”

A few months earlier, Ms. Chino, who is the store’s only employee, received a ticket for not having the store’s refund policy posted, even though she claims it was in the front window. When she brought that sign to the attention of the inspector, she said, he refused to change the citation.

The city’s public advocate, Bill de Blasio, is now getting involved after hearing from chambers of commerce, business improvement districts and small businesses at a series of roundtables he hosted earlier this year. Mr. de Blasio said businesses repeatedly mentioned the fines as among the most infuriating and time-consuming obstacles they face. His office submitted a legislative request to the City Council, the first step to introducing a bill that would allow violations from city agencies like Consumer Affairs to be contested and paid online, by mail or by phone. Fines would be differentiated more fairly between severe and low-risk violations, especially for those that don’t originate from a consumer complaint. And the bill would allow business owners with first-time, low-level citations to be given a chance to correct them before being fined.