Are double-blind trials underestimating drug effectiveness?

In a double-blind trial, patients exhibit the placebo (and nocebo) effects because of the expectation they might be on a real drug.

If expectations are so important, could it be that patients being administered the real drug don't react to it fully due to the expectation they might be on the placebo?

Addendum: Steve Waldman (of Interfluidity and Naked Capitalism) posts in the comments:

@llimllib on twitter - Bill Mill - posted a cite (in response to a tweet on this post) that seems like a nice confirmation of your conjecture. Almost perfect.

Wow.