Technically, a straight jacket is used to restrain someone from hurting themselves, and not used to completely secure them. They are only used now in those cases where a patient cannot be provided with drugs to calm them down. Most of those shows (including one past one where the world's record was a matter of seconds) looked as if the jackets were 4 sizes too large for the participant. Most lay people are not aware there are different sizes of jackets and that one size does not indeed fit all. Most audiences also do not realize that it is in fact easier to get out of the jacket upside down, despite seeing those shows.
If you are performing the jacket, and if you are to first take someone from the audience that is about your size (provided that you have a properly fitting jacket) and place them into the jacket first (if it is gimmicked, just make sure that the gimmick is not within reach of the lay person), and ask them to try to get out (if you are merely holding the straps or it takes far too long and it is not a challenge, just a demonstration. Kind of the same as holding a blindfold in front of your particpants eyes to prove one cannot see through it. It would be a waste of time to put half dollars over their eyes, tape, etc., you arew just trying to demonstrate a point), your audience will be convinced of how difficult your job is to be to get out.
Then your acting ability has to take over and you must fight your own impulses to get out quickly. Make it look as difficult as possible, get stuck part way through and struggle even further. Mentalists can do this type of escape as a demonstration of "mind over matter" and "concentration and discipline of the mind". They do prove useful, just avoid the same old gags that many other performers use and develop your own routines.
Paul Alberstat http://www.stores.ebay.ca/abstagecraft