A short absorption length ytterbium (Yb)-doped large-mode area (LMA) fiber is presented as a step forward to mitigate the stern problem of nonlinear scatterings in a tandem pumping scheme adopted for high-power fiber laser. The short absorption length was realized by incorporating high Yb concentration in the fiber core. Furthermore, by replacing the inherent silica cladding with a Ge-doped cladding, we were able to obtain low core numerical aperture (NA) and negate the detrimental effect of index-raising by high Yb concentrations. This overcomes the long-standing limitation in step-index Yb-doped fibers (YDFs) where high cladding absorption inevitably results in high NA, thus hampering single-mode operation. We report an LMA (～575μm2) YDF with NA of 0.04 and absorption of 27 dB/m at 976 nm—both traits promote power scaling of single-mode tandem pumped fiber lasers. To our knowledge, this is the highest cladding absorption attained in a low-NA step-index fiber to date. An all-fiber tandem-pumped amplifier was built using only ～14m of the YDF. The amplifier delivered a near-Gaussian beam (M2～1.27) at 836 W output power (pump power limited) with a high slope efficiency of ～83%. Thanks to the short length and the tandem pumping, no indication of limiting factors such as stimulated Raman scattering, photodarkening, and transverse mode instability was observed.