After going through this methodically, I found better solutions for a third or so of the positions, and also become much more consistent in picking the fastest solution, instead of just one of several possibilities that happened to pop into my head. It's lowered my average with 1-2 moves. And now I pass the savings on to you!

Some of the more complex ones was discovered using Ron van Bruchem's cube solver applet at speedcubing.com. It was quite a shock when it did my 20 year old 12 turn solutions in 7 turns!

aFirst the easy ones. Both pieces are in the top layer, and not adjacent.bWith the corner placed, we have these three positions

Breaks the 2x2x3 block!

cThe harder ones are when your two pieces are next to each other (and don't match up). The only easy way is to first detangle them, and then do one of the easy moves. But there are better ways. These are the top layer ones.

Note that this is an AntiSune™

You can do this with a Sune™, as seen on the Step 4 page, but I prefer this way.

This is also an AntiSune™

dWith the edge already in place a funny thing happens. The edges are good as seen from

Sequences on this page
**a1**R U R'
**a2**R U' R' U² R U R'
**a3**R U² R' U R U' R'
**a4**R U' R' U' R U R'
**a5**R U R' U R U' R'
**a6**R U R' U' R U² R'
**b1**L F² U F² U' F² L'
**b2**R U' R' U R U' R'
**b3**R U² R' U² R U R'
**c1**R U² R' U' R U R'
**c2**R U' R' U R U R'
**c3**R' U² R² U R² U R
**c4**R' U² R' U R' U' R U² R
**c5**R² U² R' U' R U' R²
**d1**R² U R² U R² U² R²
**d2**R U' R' U' R U² R'
**d3**F' U F U F' U² F
**d4**R² U² R' U' R U' R' U² R'
**d5**F² U² F U F' U F U² F

Mail me at cube@lar5.com