According to Good Housekeeping, brands of toilet paper that dissolve especially quickly include Scott 1000 one-ply, Target Up & Up two-ply, Seventh Generation two-ply, Scott Naturals two-ply and White Cloud Ultra three-ply. Contrary to expectations, one-ply toilet paper did not dissolve fastest in Good Housekeeping's tests, as of 2014.
Toilet paper dissolution rates are important because toilet paper that doesn't dissolve quickly can put stress on outflow pipes. Dissolution rates are tested to time how long toilet paper takes to dissolve in water. Other toilet paper tests include absorption, thickness of each sheet, and strength of the paper while wet and dry.