A method for inserting an insert to a tread of a tire, the method comprising - arranging available ∘ the insert and ∘ the tire comprising tread blocks forming the tread of the tire, wherein ∘ the insert ▪ extends in a longitudinal direction from a bottom of the insert to the top of the insert and ▪ has a first cross section at a first longitudinal position from the bottom and a second cross section at a second longitudinal position from the bottom, wherein the first longitudinal position is located closer to the top than the second longitudinal position and the second cross section is greater than the first cross section, and ∘ a tread block has been provided with a blind hole, the method further comprising - arranging at least a part of the insert into such a sleeve that is configured to ∘ receive at least that part of the insert that has the first cross section and ∘ support at least that part of the insert that has the second cross section in the longitudinal direction and/or a transversal direction that is perpendicular to the longitudinal direction, and - inserting the insert to the blind hole such that the bottom of the insert is inserted deeper in the blind hole than the top of the insert, characterized in that - a part of the sleeve is geometrically congruent with such a part of the insert that is left in between the first longitudinal position and the second longitudinal position. - arranging available ∘ the insert and ∘ the tire comprising tread blocks forming the tread of the tire, wherein ∘ the insert ▪ extends in a longitudinal direction from a bottom of the insert to the top of the insert and ▪ has a first cross section at a first longitudinal position from the bottom and a second cross section at a second longitudinal position from the bottom, wherein the first longitudinal position is located closer to the top than the second longitudinal position and the second cross section is greater than the first cross section, and ∘ a tread block has been provided with a blind hole, ∘ the insert and ∘ the tire comprising tread blocks forming the tread of the tire, ∘ the insert ▪ extends in a longitudinal direction from a bottom of the insert to the top of the insert and ▪ has a first cross section at a first longitudinal position from the bottom and a second cross section at a second longitudinal position from the bottom, wherein the first longitudinal position is located closer to the top than the second longitudinal position and the second cross section is greater than the first cross section, and ▪ extends in a longitudinal direction from a bottom of the insert to the top of the insert and ▪ has a first cross section at a first longitudinal position from the bottom and a second cross section at a second longitudinal position from the bottom, wherein the first longitudinal position is located closer to the top than the second longitudinal position and the second cross section is greater than the first cross section, and ∘ a tread block has been provided with a blind hole, - arranging at least a part of the insert into such a sleeve that is configured to ∘ receive at least that part of the insert that has the first cross section and ∘ support at least that part of the insert that has the second cross section in the longitudinal direction and/or a transversal direction that is perpendicular to the longitudinal direction, and ∘ receive at least that part of the insert that has the first cross section and ∘ support at least that part of the insert that has the second cross section in the longitudinal direction and/or a transversal direction that is perpendicular to the longitudinal direction, and - inserting the insert to the blind hole such that the bottom of the insert is inserted deeper in the blind hole than the top of the insert, - a part of the sleeve is geometrically congruent with such a part of the insert that is left in between the first longitudinal position and the second longitudinal position.