Yb:fiber lasers have shown excellent performance in the 980-1100 nm wavelength range. To extend the range below 980 nm, it becomes difficult to reach the transparent condition due to the smaller ratio between emission and absorption cross sections. As a result, a high demand of population inversion is needed, and the selection of pump wavelength as well as other intra-cavity parameters are crucial for lasing in the 920-960 nm wavelength range. To find a feasible solution, the pump wavelength, fiber length, and laser cavity transmittance were systematically studied. Based on the experimental result of a 960 nm Yb:fiber laser, the re-absorption loss and temperature dependent gain can be reliably modeled. The result shows promise in the development of a Yb:fiber laser at a wavelength as short as 920 nm.