A dual-mode fuel nozzle for a combustion engine, said nozzle comprising: an elongated first sleeve having an upstream end and an opposite downstream end; a supplemental sleeve disposed radially inward of said first sleeve, said first and supplemental sleeves (14, 15) defining a first fuel passageway therebetween, said first fuel passageway including an inlet and an exit, said inlet being adapted for fluid communication with a source of fuel; a second sleeve disposed radially inward of said supplemental sleeve, said supplemental and second sleeves (15, 16) defining a supplemental fuel passageway therebetween, said supplemental fuel passageway including an inlet and an exit, said inlet being adapted for fluid communication with a source of fuel; a third sleeve disposed radially inward of said second sleeve, said second and third sleeves (16, 18) defining a cooling fluid passageway therebetween, said cooling fluid passageway having an inlet and an exit; and a cooling fluid conduit adapted to fluidly connect said cooling fluid passageway with a source of cooling fluid, said conduit having a conduit entrance located upstream of said first fuel passageway exit and a conduit exit in fluid communication with said cooling fluid passageway inlet, whereby said cooling fluid conduit, said cooling fluid passageway, and said fuel passageways (22, 23) cooperatively ensure that cooling fluid passing through said cooling fluid passageway exit is substantially fuel-free during operation, wherein said first sleeve cooperatively forms an outer passageway with an outer boundary member (12, 82) spaced radially outward from said first sleeve, said outer passageway being in fluid communication with said first fuel passageway exit, said outer passageway including an upstream entrance and a downstream exit, said entrance being adapted for fluid communication with a source of air, wherein said nozzle includes a set of premix air apertures for supplying air from said source of air to said entrance of said outer passageway, wherein said nozzle includes a set of supplemental fuel apertures for supplying fuel from a source of fuel to said inlet of said supplemental fuel passageway, wherein said nozzle includes a set of first fuel apertures for supplying fuel from a source of fuel to said inlet of said first fuel passageway, wherein said premix air, supplemental fuel, and first fuel apertures (48, 49, 50) extend longitudinally in said nozzle through a fluid supply hub of said nozzle, wherein said cooling fluid conduit is disposed within said fluid supply hub and is oriented in a substantially radial relationship with respect to a longitudinal axis of said nozzle and lies between said premix air, supplemental fuel, and first fuel apertures (48, 49, 50), wherein said conduit entrance is located radially-outboard of said first fuel passageway and said conduit exit is located radially-inboard of said first fuel passageway. an elongated first sleeve having an upstream end and an opposite downstream end; a supplemental sleeve disposed radially inward of said first sleeve, said first and supplemental sleeves (14, 15) defining a first fuel passageway therebetween, said first fuel passageway including an inlet and an exit, said inlet being adapted for fluid communication with a source of fuel; a second sleeve disposed radially inward of said supplemental sleeve, said supplemental and second sleeves (15, 16) defining a supplemental fuel passageway therebetween, said supplemental fuel passageway including an inlet and an exit, said inlet being adapted for fluid communication with a source of fuel; a third sleeve disposed radially inward of said second sleeve, said second and third sleeves (16, 18) defining a cooling fluid passageway therebetween, said cooling fluid passageway having an inlet and an exit; and a cooling fluid conduit adapted to fluidly connect said cooling fluid passageway with a source of cooling fluid, said conduit having a conduit entrance located upstream of said first fuel passageway exit and a conduit exit in fluid communication with said cooling fluid passageway inlet,