Absolute instabilities in shear flows can cause a catastrophic breakdown into a new unsteady state, or even into turbulence. We demonstrate that in a double-diffusive channel flow with a viscosity stratification across the channel, rapidly growing absolute instability may be obtained at Reynolds numbers of a few hundreds. The instability is much weaker in an equivalent single solute fluid with the same viscosity contrast, or even in one which is made up only of the more dangerous of the two diffusing species. This is a novel characteristic of double-diffusive systems driven by viscosity, rather than density variations. Convective instabilities too are stronger in the double-diffusive case. © 2012 American Institute of Physics.