We use a differential microbiome-propagation method to artificially select for rhizosphere microbiomes that confer salt-tolerance to the model grass Brachypodium distachyon. To optimize methods, we conceptualize microbiome-selection within a host-focused quantitative-genetic framework (Mueller & Sachs 2015), rather than within a multi-level selection framework ('artificial ecosystem selection' sensu Swenson et al 2000). Artificial microbiome-selection represents a special case of indirect selection that quantifies host phenotype (but does not measure microbiome properties directly) and uses host phenotype to infer presence of microbiomes that interact beneficially with a host; we have called this indirect-selection scheme previously host-mediated indirect selection on microbiomes. We improve on the methods of Swenson et al by modifying several protocol steps to maximize evolutionary changes due to differential microbiome-propagation, while minimizing some (but not all) ecological processes affecting microbiome composition. Specifically, our methods aim to improve microbiome perpetuation and response to artificial microbiome-selection by (a) controlling microbiome assembly when inoculating seeds; (b) low-carbon soil to enhance host-control during initial microbiome assembly and subsequent microbiome persistence; (c) microbiome-fractionation to propagate and select only on bacterial and viral (but not fungal) microbiome components; and (d) ramping of salt-stress between selection-cycles to minimize the chance of either under-stressing or over-stressing plants. Depending on salt-stress and control treatments, our protocol generates microbiomes that enhance plant fitness after only 1-3 rounds of host-mediated indirect selection on rhizosphere microbiomes. When testing microbiomes after nine rounds of differential microbiome propagation, the effect of bacterial microbiomes selected to confer tolerance to sodium-sulfate stress appears specific (these microbiomes do not confer such tolerance under aluminum-sulfate stress), but the effect of microbiomes conferring tolerance to aluminum-sulfate stress appears non-specific (selected microbiomes ameliorate both sodium- and aluminum-sulfate stresses). Ongoing metagenomic analyses of the artificially selected microbiomes will help elucidate metabolic properties of microbiomes that confer specific versus non-specific salt-tolerance to plants.