Pun Bandhu’s training at the prestigious Yale School of Drama didn’t help much with the skill he needed for so many auditions after graduation – the “Asian accent”.

The Thai American actor – who has appeared in a wide range of TV shows and films over the last 15 years – said he was once told that an accent he used for a Thai character, modeled after his parents, was not working for an “American ear”. Instead, the director went with a Chinese accent.

While much of the recent debate around Asian representation in Hollywood has centered on whitewashing – when white actors are cast to tell Asian stories – working actors said a lack of opportunity was only one part of the problem. Asian American actors said they rarely, if ever, got auditions for leading roles, and when they did get parts, they were frequently secondary to the plot or portrayed offensive tropes.

Asian men said they were often relegated to roles as tech nerds, assistants, doctors – sometimes highly emasculated, desexualized characters. Asian women, meanwhile, regularly go up for parts as masseuses and sex workers or characters described as submissive, fragile or quiet.

“We’re the information givers. We’re the geeks. We’re the prostitutes,” Bandhu said. “We’re so sick and tired of seeing ourselves in those roles.”

Asian American actors said there had been an increase in diverse roles in recent years, though, and some were hoping that the recent controversy surrounding Ghost in the Shell – which starred Scarlett Johansson in the remake of an anime classic – would inspire directors and producers to stop whitewashing Asian characters. The film flopped, earning only $19m in the US in its opening weekend, a small sum relative to its $110m budget. One Paramount executive said the casting backlash was partly to blame.

Emma Stone, Matt Damon and Rooney Mara have all faced whitewashing criticisms for their roles in films that ultimately performed badly at the box office. But improving diversity and representation in film and television goes far beyond avoiding casting blunders in commercial movies.

“We’re so desperate for opportunities,” said Kanoa Goo, a mixed-race actor who is Chinese, Hawaiian and white. “Often it’s pretty one-dimensional. It’s the tech computer analyst who doesn’t have much to say. His role is really just in service of the leads.”

Goo, who appeared in the 2016 film Other People, said most of his auditions were for parts specified for Asians or non-white actors, and sometimes those roles could feel tokenized – designed to check off the diversity box.

“Within the sort of marginalized group of diverse actors, Asian American actors are still at the very bottom. They are still the underdog,” he said.

Asian characters made up only 3%-4% of roles in scripted broadcast and cable shows in the 2014-15 season, according to a recent University of California, Los Angeles (UCLA) report. Of the top 100 films of 2015, 49 had no Asian characters, and zero leading roles went to Asians, according to another study.

In addition, “the quality of roles is problematic,” said Darnell Hunt, a UCLA professor who co-authored the diversity report.

Lynne Marie Rosenberg, an actor who runs a Tumblr called Cast and Loose, which publishes offensive character “breakdowns” from auditions, said she frequently saw casting calls that listed nearly all ethnicities – except Asian.

“The number one problem is invisibility,” she said.

There is also sometimes a comical overgeneralization of Asians. Rosenberg provided an example of an Asian character described as an artist who remained “focused while he composes his drawing”. The breakdown added: “Makes you wonder what kind of life he had back in Asia.”

Another film sought an Asian rapper who could “rhyme a few lines with an accent or in any Asian language”. A breakdown for a South Korean character sought a female actor age 18 to 25 to play a 17-year-old who is “really only good at being pretty”.

One character in another project was described as “Asian. Petite. Slim. Fragile.” The storyline: “A rich man keeps a woman in the basement.”

Kal Penn, an Indian American actor known for his roles in the Harold & Kumar movies and the TV series House, recently made waves when he tweeted racist script excerpts he had received, such as “Gandhi lookalike”, “snake charmer” and “Pakistani computer geek … in a perpetual state of perspiration”.

Atsuko Okatsuka, a Japanese standup comedian and actor, said she had gone up for roles that were clearly terrible matches for her – where it seemed the only reason she was called in was her race. She recalled one “Japanese schoolgirl” character for whom, she said, “I had to squeal a lot and speak in a very high-pitched cadence in Japanese. And giggle.”

Okatsuka said she had also lost lead Asian roles to mixed-race women who looked much more white. The message she received was: “You’re more fitting for this more soft-hearted, kind, kimono-wearing friend of the lead.”

Breakdowns that specify characters as half-Asian for seemingly no plot reason were also hurtful, she said: “They’re trying to say they want somebody better looking than east Asian.”

Camille Chen, a Taiwanese American television actor, said she had been getting auditions for a wide range of parts and that her ethnicity had become an advantage as more industry leaders recognized the importance of diversity.

But despite the significant progress – when she started her career 13 years ago, she felt she had no choice but to go up for the masseuses and prostitutes – Chen acknowledged that she never got to audition for principal characters in films. “I wish they would open their minds to having Asian Americans lead.”

Vinny Chhibber, an Indian American actor, said when he first started acting, he often went up for “terrorist #1” or “socially incompetent emasculated Asian stereotype with an accent”.

As a writer and producer, Chibber said he also often heard prejudices emerge in casting meetings, where someone might say: “Well, if you cast a Chinese girl, it’ll change the story.”

Chibber said he now turned down auditions for roles that promote stereotypes, in part because he understood how damaging those characters could be: “The work we do has such a profound impact on the way people see the world.”

The lack of three-dimensional Asian characters makes the whitewashing choices all the more painful for actors and audiences, Bandhu said.

“When a white actor gets the role, it denies us our bodies and it denies us our voices.”