In the most developed fiber amplifiers, optical pump power is introduced into the ~400μm-diameter, 0.46NA first cladding of the double-clad, Yb-doped, gain fiber, using a (6+1):1 multi-mode fiber combiner. For this configuration, the core diameter and numerical aperture of the pump delivery fibers have maximum values of ~225μm and ~0.22, respectively. This paper presents the first fiber-coupled laser-diode pump module emitting more than 1kW of claddingmode- stripped power from a detachable 225μm, 0.22NA delivery fiber at 976nm. The electrical-to-optical power conversion efficiency at 1kW is ~50%. The FWHM spectral width at 1kW output is ~4nm and has an excellent overlap with the narrow absorption spectrum of ytterbium in glass. Six of these pump modules attached to a (6+1):1 multimode combiner enable a 5-6kW, single-mode, Yb-doped fiber amplifier.