A fibrous structure testable in a series of run-off tests, wherein each run-off test includes exposing the fibrous structure to a volume of a test solution and the fibrous structure initially is hydrophobic and has been treated to be hydrophilic, wherein the fibrous structure exhibits a run-off level that is less than 5 percent by weight throughout a series of run-off tests, and wherein the series starts with a first run-off test and ends with a fifth run-off test.