As slvoid says, "trim" your front derailer (which is a bit of a trick to master in STI---or RapidFire, come to think of it!).
If that fails, you may need to make some minor adjustments in the system, usually by "tweaking" the cable at the adjuster(s).
You should, in a "double", be able to use all but the largest rear cog with the 'big" ring; the opposite is true with the "small" ring. However, it is more "efficient" to shift in front once you are much past the "middle cog" in the rear in either direction: the chain "running" angle is less extreme and reduces wear on the entire system.