This double camera on 16th Street NW can find speeding cars in both the southbound and northbound lanes. (Michael S. Williamson/The Washington Post)

There were nearly 2.5 million crestfallen moments — instances when people said “Oh, dang” or worse — last year in D.C. when a ticket appeared under the windshield wiper blade, in the outstretched hand of a police officer or came by mail as the handiwork of a heartless camera beside the road.

Tickets for illegal parking, moving violations and those generated by automatic red light and speed cameras make all of their recipients unhappy, but most people mutter a few impolite comments and pay the fine.

Most, but not everybody.

Some people who felt they’d been done an injustice challenged their ticket, and often they won, according to an analysis by AAA Mid-Atlantic.

“These are the true believers. These are the people who have explanations. These are people who have photos to back up their claims,” said John B. Townsend II, spokesman for the AAA.

A review of D.C. Motor Vehicle Administration data for fiscal year 2015 shows that the easiest ticket to beat was one handed through the driver-side window by a police officer for a moving violation. About 40 percent of the people who get one take it to court (although court, in fact, is a hearing before an adjudication examiner in a setting that looks nothing like a courtroom).

Of the 27,136 people who contested a moving violation last year, 71 percent got their ticket dismissed. One reason for that may be that in 6,596 cases the officer who wrote the ticket wasn’t able to make the hearing. The Metropolitan Police Department said it would look into why that was the case.

“Motorists are more inclined to fight citations for moving violations, perhaps because they want to avoid points on their driving record, and to avoid a costly increase in their car insurance rates,” Townsend said.

Tickets for illegal parking make up 70 percent of all tickets issued in the District. About 9 percent of the people who receive one file an appeal, and more than half of them succeed in getting them dismissed.

The ticket people are least likely to beat is the one generated by a camera catching drivers who run red lights or speed. Only six percent of the people who received tickets in the mail challenged the cameras, and 80 percent of those drivers were ordered to pay the fine, according to the AAA analysis.

The number of successful challenges to camera tickets dropped from 19 percent in 2014 to 6 percent last year.

The number of tickets contested by the drivers who received them has dropped in each of the past three years, with 114,516 fewer appeals filed in 2015.

The DMV said procedures put in place in 2014 allow drivers additional time to submit necessary documentation to contest a ticket.

DMV spokeswoman Vanessa E. Newton said that drivers who present persuasive evidence are likely to sway the hearing officers.

“In most cases, drivers will not submit adjudication requests for tickets for which there is no evidence for dismissal,” Newton said. “Therefore, the adjudication dismissal rate should always be higher than the upheld rate.”