I've always thought that these sort of trials should use an initial wash-out period to weed out the placebo responders. You need to avoid participants knowing for sure they are on a placebo, so maybe a design like this:
Washout period has 3 arms:
10% placebo arm 1 10% drug arm 2 80% placebo arm 3
After the washout period you discard patients from placebo arm 3 that had a response, and you re-randomize the remaining patients from arm 3 to placebo arm 1 or drug arm 2.