We report on a Yb3+:KGW self-Raman laser operating at 1096 nm. A 100 ??m fiber-coupled diode end-pumped configuration is used to generate a fundamental emission wavelength that strongly depends on internal resonator losses. Stokes emission at 1096 nm is achieved with a slope efficiency of 42 ?? 8%, an optical conversion efficiency of more than 32% and a maximum output power of 4.5W for quasi-continuous operation (1 ms pulses). The explored Stokes conversion of 89 cm???1 shows excellent laser characteristics, indicating that this still little explored Stokes shift could pave the way to continuous-wave Raman frequency-comb lasers.Funda????o de Amparo ?? Pesquisa do Estado de S??o Paulo (FAPESP)Conselho Nacional de Desenvolvimento Cient??fico e Tecnol??gico (CNPq)FAPESP: 17/10765-5CNPq: 1420502015-6