The accompanying music video for "Possibly Maybe" was directed by French artist Stéphane Sednaoui, for a song that is about his failed relationship with Björk. The singer and the director had previously worked together in the music video for "Big Time Sensuality". In the clip, she appears "as a goddess, floating out from a numinous light-streaked background." It shows Björk in a variety of different rooms in an apartment. She is primarily shown in a large, stylish bedroom with modern décor. These scenes are intercut with shots in ultra-violet lighting (which subsequently causes everything to appear in day-glo colours). She is also shown in three other rooms: submerged in the bathtub of a bathroom; an Asian-themed room; and a room full of stereo equipment. These scenes are intercut with an angelic image of her dressed all in white, floating out of a blue sky with the sun behind her. The majority of objects appearing in the video were Björk's own.