The Strip the Willow

Figure 1:  1st couple swing each other around, using two hands crossed (R in R, L in L)
Figure 2:  First lady turn next man down using L  hand or L arm hold, then turn first man, by the R arm to the next man down, who she turns by the L, then partner etc. all the way down to the bottom of the set.
Figure 4: Progressing up the set: First M turn next woman up using L hand or L arm hold, then turn first woman by the R arm to the next woman up, who he turns by the L, then partner etc. all the way up to the top  of the set.
Figure 5: The first couple works their way back down the set, man turning each woman by the L at the same time as the lady turns each man by the L. 1st couple turns each other by the R between each R hand turn.
Figure 6: 1st couple swing each other around, using two hands crossed (R in R, L in L)

The new top couple can start the dance once the old 1st couple has moved down a few couples in figure 5.  There's no need to wait until the other couple has reached the bottom.