The free double principle applies as well in most cases when the opponent makes a hand. I think of it as "the cheap double".
I worked out this strategy spending several hours on Excel about nine years ago, but seem to have lost my notes on it. No one has ever checked my work on this, so please feel free to work it out mathematically and if I'm wrong, come back on here and tell me I'm full of it.
DD any hand with any dealer upcard and opponent total 16 or less.
DD on hard 19 with dealer upcard 2-6 and opponent total 17 or higher.
DD on hard 18 with dealer upcard 7 and opponent total 18 or higher.
DD on hard 20 with dealer upcard 8-A and opponent total 17 or higher.