Supergirl encounters some people who she thinks she knows but can't remember. Eventually it gets too much for her and she faints. She wakes up in the next issue under a pile of ruble.

Supergirl is fighting a bunch of insects with her ally who gets in trouble. When she tries to help him she is subdued by the insects but how is not shown. She wakes up later, restricted, by the Insect Queen.

I like the humnor of it more than anything. Source: http://optimuspraino.deviantart.com/

I like this one because the pose is different from similar ideas where the victim is held facing up. Source: mhunt.deviantart.com

Hime ( in this manga, she is known as "Supergirl" ) gets kidnapped while in a hospital. Her assailant comments that she was able to smell the chloroform, even in a hospital! Not a bad scene.

Supergirl and The Flash overcome by some alien space ray...I gave it an extra star for the great cover, which, while not "sleepy" , is cool peril. Source: Some Blog

Source: dccomics.com Supergirl #46, Blackest Night Superman #2.

Source: mhunt.deviantart.com. Please check out MHunt's art page, thanks!

Nice 3d scene, too bad about the skirt not rendered well. Kinetics has appeared on the Femforce comic.

The iconic "Death of Supergirl" cover. Art by George Perez.

A famous mural by Alex Ross, recreating a cover from Crisis on Infinite Earths. The picture was found on this site: http://hallofheroes.free.fr/Html/goodies/posters.htm. There is a much higher resolution version there.

Supergirl gets into a tough fight with Maelstrom (a very strong female villain). She is rendered unconscious, but Superman comes and rescues her. The defeat really hurts Supergirl's ego though.

Some original art by an artist named Axel Pablo. You can see some of his art at: http://axelpablo.deviantart.com/ I only included his sleepy art. He has a lot of bondage art too.

This was donated by the artist Monsieur Paul as a gift! Support Monsieur Paul's work: https://www.patreon.com/mpcomics

Supergirl manages to wake up from the gas (issue 56). She ties up the female villain.

This is a pretty famous cover. Two really sexy superheroines bound and gagged! There is also a nice unconscious carry of Supergirl near the end.

A female scientist is hit over the head with a blackjack. When she wakes up, she's bound and gagged and taken hostage.

Supergirl sucker punches a woman named Blithe as she was walking out of the ladies room.

Supergirl knocks herself out.

Supergirl (as Linda Danvers) is hit over the head with a crowbar and kidnapped. Of course, she escapes later on.