Unbandaged Big Block. Problem #1: Everything solved except for 2 edges needing to flip. Problem #2: All edges oriented correctly but two corners needing to swap. Solution: Trash the edge orientation, and mess around until the corners could be solved. Then use setup moves with the unbandaged block to solve the edges.

More observations, discoveries, happy little accidents. :D To cycle 3 edges—UB to UF to DR—do the thing you do when solving corners first and you are getting all X's and there is 1 pair. Then do U2. Then do it all again. To cycle UB to UF to UR, start and end with R2.

That is, to cycle UB to UF to DR do (R2 U R2 U' R2 U R2 U' R2 U2) x 2. This is much easier to execute than the edge 3-cycle figured out while doing Big Block and could be used with Big Block as well as this one.

Think Corners First. You have the upper and lower X's and are going for all X's. If you have stumbled across this page and are not familiar with the Corners First Method, check out the 2x2x2 Cube Solution page.

You have 4 pairs around the bottom. (R' F R F') (R U R') (R U R' U R U2 R') to get 5.

You have 5 pairs, 2 on the left. (R' F R F') (R U R') (R U R' U R U2 R') to get all.

You have 2 pairs, 1 on the upper right, 1 on the lower left. (R' F R F') (R U R') (R U R' U R U2 R') to get 1.

Of course the algorithm can be shortened to R' F R F' R U2 R' U R U2 R' if you are just wanting a shorter algorithm to learn, but I don't see it as an algorithm to learn. I see it as EPS to shake up the corners; URD to put the bottom one back; Sune to reorient the top ones.