Solving the 1-nt Bulge Zigzag
See also: Brourd's Zigzag Catalog
The 1-nt bulge zigzag has several solutions, each requiring at least 2 GC pairs. In each case, the zigzag can be thought of as an especially unstable 2-2 loop that has collapsed on itself. For a list of zigzag sequences, follow the above link.
Solving the 2-1 Loop Zigzag
The 2-1 loop zigzag has a large number of solutions and requires at least 1 GC pair to solve. This loop can be considered an unstable 4-4 loop that has collapsed on itself. To solve the 2-1 loop zigzag, it is necessary to avoid boosting the 4-4 loop that would form by breaking the isolated base pair. The GA/G mismatch and GC/A mismatch both selectively stabilize the 2-1 loop.