There is increasing interest in artificially selecting or breeding microbial communities, but experiments have reported modest success and it remains unclear how to best design such a selection experiment. Here, we develop computational models to simulate two previously known selection methods and compare them to a new "disassembly" method that we have developed. Our method relies on repeatedly competing different communities of known species combinations against one another, and sometimes changing the species combinations. Our approach significantly outperformed previous methods that could not maintain enough between-community diversity for selection to act on. Instead, the disassembly method allowed many species combinations to be explored throughout a single selection experiment. Nevertheless, selection at the community level in our simulations did not counteract selection at the individual level. Species in our model can mutate, and we found that they evolved to invest less into community function and more into growth. Increased growth compensated for reduced investment, however, and overall community performance was barely affected by within-species evolution. Our work provides important insights that will help design community selection experiments.