The week-old redesign of quick-messaging service Twitter was meant to simplify its tools and make it more accessible to newbies. But it has had some unintended consequences.

Independent developers of applications that tie into Twitter’s network say they have experienced significant accelerations in downloads and revenue since Twitter 4.0 launched last week.

When addicts of the social network got their hands on the new version, many recoiled upon seeing the changes. They were especially vocal about the loss of some features in Twitter’s mobile apps and about the private-message tab being hidden within another menu.

So thousands flocked to the various app stores to get third-party apps that look more like the previous version of Twitter. Some of the most popular apps cost a few dollars, unlike the free app made by Twitter.

Tweetbot, an anime-themed app for the iPhone, more than doubled its usual revenue just after Twitter’s major redesign, said Paul Haddad, a co-founder for app maker Tapbot. When the small developer cut the price of Tweetbot in half on Friday, to 99 cents, revenue increased more than tenfold, Haddad said.

Independent trackers of app downloads verify that Tweetbot and others experienced big gains.

“Word of mouth really goes a long way on Twitter,” Haddad wrote in an e-mail.

The maker of another popular app, Twitterrific, saw a “bump” after the Twitter changes, which carried through to this week, said Craig Hockenberry, the head of app maker Iconfactory. This effect is common, but short-lived, after a major change to Twitter, he said.

Twitterrific, which offers a free version with ads or a full version for $4.99, experienced a similar boost in March after Twitter updated its iPhone app with a much-maligned feature called the Quick Bar, Hockenberry said. The Quick Bar, which critics dubbed Dick Bar after Twitter CEO Dick Costolo, added an ever-present ticker showing trending topics and ads. Within a month, Twitter had removed the feature.

“Please stop complaining about the new Twitter app,” Haddad wrote on his Tapbot Twitter account last week. “They might revert back, and I’m really enjoying the increase in sales.”

For a relatively new Twitter app, like Twittelator Neue, the backlash provided some much-needed attention. That app, which costs $1.99, has seen about three times as many downloads in the week since Twitter 4.0.

“We’ve definitely seen a spike since Twitter updated their official client,” Ollie Wagner, the Twittelator developer, wrote in an e-mail. “Changes like the ones they’ve made tend to be quite polarizing, oftentimes magnetizing audiences towards newer third party clients.”

In March, during the Quick Bar fiasco, Twitter began discouraging makers of these types of apps from pursuing development. Ryan Sarver, a leader on Twitter’s developer relations team, wrote then in a memo to partners that they should not be building software that reproduces the functions of a standard Twitter app.

“We need to move to a less fragmented world, where every user can experience Twitter in a consistent way,” Sarver wrote. “This is already happening organically — the number and market share of consumer client apps that are not owned or operated by Twitter has been shrinking.”

As that number seems to grow slightly, it’s unclear whether Twitter’s stance has changed. A Twitter spokeswoman declined to comment, and Sarver didn’t immediately respond to a request for comment.