Experiments with photofits show that even subtle mistakes in the shape, length and colour of hair can completely throw crime witnesses.
A team at Stirling University found that witnesses tend to place more reliance on hair than facial features - despite the fact hair is so easy to alter.
The psychologists conclude that police forces might be better off producing photofits of bald suspects than inaccurate images of crooks with hair.
Wigs, hair dye and radical cuts are a staple of the thriller genre. In 2002's The Bourne Identity Matt Damon helps female lead Franka Potente dye her hair from red to black as they evade the authorities.
But the Stirling research, which involved getting volunteers to produce photofits of celebrities, suggests the effort is well worth it.
These were shown to another team who had to identify the famous person.
Slight mistakes in representing the celebrities' hairstyles were often enough to throw the second group off the scent.
Dr Alex McIntyre, of Stirling University's Psychology department, is part of a team examining how people remember faces.
She said: "Your memory and perception tends to be dominated by the hair. You can make a very quick and rapid judgement from hair.
"The witness to the crime might be overly influenced by the hair. It's important to bear in mind, especially with criminals, that they can change their hair or put on a hat."