The Jessica (jiri) moves for placing an edge and matching corner without using free slots are well documented on other sites. That technique can be extended as described on this site by doing non-matching pairs - this still involves placing one corner and one edge at a time. There are some short solutions for doing the first slot (since all the other slots are free slots) that may be of interest.
Sometimes corners may already be placed, in which case placing 2 edges at once may be desirable. Some of these I have used Rons applet to determine.
If edges have already been placed then it may be desirable to place 2 corners at once. This would be desirable, but given the low frequency of occurance and the number of different algorithms that would need to be remembered I don't think it worth attempting.
Many sites have lists of algorithms, the following ones hopefully cover situations not covered on those.
The applets used below were created by Lars Petrus based on applets written by Karl Hornell.
One of the trickier situations to deal with is when a corner is showing the D colour on the U face. There are a number of shortcuts available depending upon where the edge piece is and which free slots are available.
First group...
For this group of solutions the corner being placed is in the U layer with the colour of the D face being on top. The edge is in the middle layer, and is considered flipped if the colours don't match the centre pieces (or the opposite centre piece colour). The target slot for the corner-edge pair if FL. Those marked (*) only affect the slot the edge is in and the target slot. This covers the positions where the edge piece is in a slot different to the target slot.
Target slot FL: Edge piece in FR slot: edge non-flipped corner FLU - F2UF2U'F2 (*) corner FRU - F2LF2L' (*) edge flipped corner FLU - L'F'L2UFL (back right unaffected) R'FR2U'R'U2F' (*) Edge piece in BR slot: edge non-flipped corner FLU - F2DR2D'F2 (*) L2D'B2DL2 (*) edge flipped corner BRU - FR'URF' (*) L'BU'B'L (*) Edge piece in BL slot: edge non-flipped corner FLU - L2U'L2UL2 (*) L'F'L2FL (*) corner BLU - L2F'L2F (*) edge flipped corner FLU - FLF2U'L'F' (back right unaffected) BL'B2UBU2L (*)
There are a few more short sequences but they affect other slots, so I think that the above are the most useful.
Second group...
This next group again has the corner piece upside down in the U layer, but this time the edge piece is in place in the target slot. To keep you on your toes, the target slot is FR instead of FL. The situations where the edge piece is flipped are trivial, so only non-flipped are given.
Target slot FR: using free slot BR corner FRU - nothing better than not using free slot corner FLU - R2F'U2FU2R2 corner BLU - F'RB'R'BF BF2UB'U'F2 corner BRU - no quick solutions using frees slot BL no quick solutions using free slot FL corner FRU - nothing better than not using free slot corner FLU - no quick solutions corner BLU - RF'LFL'R' L'R2U'LUR2 corner BRU - F2RU2R'U2F2 and finally, using no free slot corner FRU - R2UR2UR2U2R2 corner FLU - RU'BU2B'UR' corner BLU - RU'BUB'UR' F'UL'U'LU'F corner BRU - F'UL'U2LU'F
If the corner is in place but rotated, and the edge piece is in a different slot ie in the middle layer, then the procedure of bringing the corner to the top layer, then the edge and finally placing the pair can be followed but is long winded. eg do the moves RU'R2F'RLU2LF' on a solved cube, then (RU2R')(L'UL)(F'U2F) will solve using this way. There are shorter methods for every scenario except the one just given, and these are given below.
The target slot is FR in all these examples, and none of them affect slots other than the target slot and the slot the edge is in.
Edge in FL: flipped - corner rotated +1 RU'R2D'F'DR corner rotated +2 no good solutions unflipped - corner rotated +1 F'UR'F2RF corner rotated +2 R2DRD'RUF2 F2L'U'LF2UF2 Edge in BL: flipped - corner rotated +1 RU2B''UBR' F'LUL'U2F corner rotated +2 RB'U'BU2R' F'U2LU'L'F unflipped - corner rotated +1 F'UF'D'L2DF2 corner rotated +2 RU'RDB2D'R2 Edge in BR: flipped - corner rotated +1 R'U2FRF2U'F corner rotated +2 F'UF2DRD'F' unflipped - corner rotated +1 F'UBUB'UF BU'F'U2B'UF F2D'F'DF'U'R2 R2BUB'R2U'R2 corner rotated +2 RU'FR2F'R' F'U'BU2B'F'
Only some of the possible cases are documented below. The rest need to be determined. Any contributions to ways of doing the moves will be gratefully received - some have already been contributed by Mirek Goljan.
Case One:
LB2DF2D'B2L'/R'B2D'F2B2R
Case Two:
FL2DFD'F'L2U'F'/F'R2D'F'DFR2UF
Case Two alternative algorithms:
FUL2FDF'D'L2F'/F'U'R2F'D'FDR2F
Case Three:
F2U2FU2F2/F2U2F'U2F2
Case Three alternative solutions:
B2D2FD2B2/B2D2F'D2B2
Case Four:
F'U2R'FLF2RL'F
New ones: FLR'FL'RU'F'and from U2:FLR'F'L'RUF'
FL'RU2LR'F
More examples to follow: please send me move sequences if you have them.
Examples to follow: please send me move sequences if you have them.