  We extend Lerner's recent approach to sparse domination of
Calder\'on--Zygmund operators to upper doubling (but not necessarily doubling),
geometrically doubling metric measure spaces. Our domination theorem is
different from the one obtained recently by Conde-Alonso and Parcet and yields
a weighted estimate with the sharp power $\max(1,1/(p-1))$ of the $A_p$
characteristic of the weight.
