Back in the '60s I was taught about the smile technique and I never really got the tone I wanted. More recently, during my comeback, my research has shown me to liken the embouchure to the neck of a ladies drawstring purse. Think of the mouth as two concentric rings with the muscles around the mouth as the drawstring and the mouth (lips) as the floppy bit beyond the drawstring. I find that to tension the corners of the drawstring - the edges of the mouth - and leave to lips relaxed, is a great place to start. This allows the lips to vibrate with or without pressure between them, as the player chooses while providing the muscular support necessary for proper embouchure control.
Does that make any sense at all - for once I'm struggling to create a word picture for you. I keep thinking of a cat's arse and that is just distracting.