On Tuesday, the LGBT advocacy group GLAAD released its second-ever annual run-down of depictions of gay, bisexual and transgender characters in major Hollywood movies, the Studio Responsibility Index. The organization took a look at 102 major studio releases from 2013, and found that not much had changed: about 17% of the movies examined contained LGBT characters, versus last year’s 14%; about 7% of them passed the “Vito Russo Test” — GLAAD’s way of measuring whether a depiction is both positive and substantial — versus last year’s 6%.

Though the number has increased slightly in both counts, only one character out of a whole cast is needed to move a movie into the “yes” column — and many of the films that don’t pass the Vito Russo Test get a “no” for actually being offensive, not just for lacking an LGBT character. (Among the offenders: The Hangover Part III for the character of Leslie Chow and Grown Up 2‘s “recurring jokes about a female bodybuilder character secretly being a man.”) In addition, GLAAD found that none of the LGBT characters counted were leads, the group was not very diverse (three-quarters of the gay characters were white) and the genres where Hollywood money is most readily spent, such as action, are the least likely to feature LGBT characters.

But despite numbers that GLAAD calls “depressing” in its findings, there were a few bright spots. Notably, in a studio-by-studio tally, Sony Columbia became the first major studio in the study’s history to receive a “good” score, after being marked “adequate” last year, on the strength of The Mortal Instruments: City of Bones and Battle of the Year, both of which pass the Vito Russo Test. 20th Century Fox and Disney both went from “failing” to “adequate.” The number of transgender characters overall also increased from zero to two.

The reason GLAAD takes the time to track these movies, the report explains, is that Hollywood films are — in addition to being entertaining — capable of spreading ideas worldwide. When a gay character gets significant screen time but perpetuates stereotypes (as in the case of Riddick, GLAAD points out, where a major lesbian character is routinely insulted and later successfully seduced by the ultra-macho protagonist) that may be worse than having no depictions of gay people at all.

“These studios have the eyes and ears of millions of audience members, and should reflect the true fabric of our society,” said GLAAD CEO and President Sarah Kate Ellis in a statement announcing the report’s release, “rather than feed into the hatred and prejudice against LGBT people too often seen around the globe.”

Write to Lily Rothman at lily.rothman@time.com.