A method of treating pulp to reduce use of halogen-containing oxidants, the method including a delignification process to delignify the pulp, the delignification process comprising: adding a peracetate oxidant solution to a pulp at a primary addition point and contacting the pulp with the peracetate oxidant solution; and mixing the pulp with the peracetate oxidant solution; characterized by: the peracetate oxidant solution formulated to generate singlet oxygen as a reactive oxygen species in the resulting mixture, wherein the peracetate oxidant solution comprises, as added to the pulp: a pH in a range of from pH 10 to pH 12; peracetate anions and a peracid with a molar ratio of peracetate anions to peracid of from 60:1 to 6000:1; and either no hydrogen peroxide or hydrogen peroxide wherein a peracetate anion to hydrogen peroxide molar ratio is greater than 16:1; and after a period of time following the adding, separating from the pulp an oxidant liquor containing residual active oxidant from the peracetate oxidant solution and conveying the oxidant liquor to a secondary addition point, upstream of the primary addition point, where the pulp and the oxidant liquor are contacted and mixed. adding a peracetate oxidant solution to a pulp at a primary addition point and contacting the pulp with the peracetate oxidant solution; and mixing the pulp with the peracetate oxidant solution; characterized by: the peracetate oxidant solution formulated to generate singlet oxygen as a reactive oxygen species in the resulting mixture, wherein the peracetate oxidant solution comprises, as added to the pulp: a pH in a range of from pH 10 to pH 12; peracetate anions and a peracid with a molar ratio of peracetate anions to peracid of from 60:1 to 6000:1; and either no hydrogen peroxide or hydrogen peroxide wherein a peracetate anion to hydrogen peroxide molar ratio is greater than 16:1; and after a period of time following the adding, separating from the pulp an oxidant liquor containing residual active oxidant from the peracetate oxidant solution and conveying the oxidant liquor to a secondary addition point, upstream of the primary addition point, where the pulp and the oxidant liquor are contacted and mixed. the peracetate oxidant solution formulated to generate singlet oxygen as a reactive oxygen species in the resulting mixture, wherein the peracetate oxidant solution comprises, as added to the pulp: a pH in a range of from pH 10 to pH 12; peracetate anions and a peracid with a molar ratio of peracetate anions to peracid of from 60:1 to 6000:1; and either no hydrogen peroxide or hydrogen peroxide wherein a peracetate anion to hydrogen peroxide molar ratio is greater than 16:1; and a pH in a range of from pH 10 to pH 12; peracetate anions and a peracid with a molar ratio of peracetate anions to peracid of from 60:1 to 6000:1; and either no hydrogen peroxide or hydrogen peroxide wherein a peracetate anion to hydrogen peroxide molar ratio is greater than 16:1; and after a period of time following the adding, separating from the pulp an oxidant liquor containing residual active oxidant from the peracetate oxidant solution and conveying the oxidant liquor to a secondary addition point, upstream of the primary addition point, where the pulp and the oxidant liquor are contacted and mixed.