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As cloud resources and applications grow more heterogeneous, allocating the right resources to different tenants' activities increasingly depends upon understanding tradeoffs regarding their individual behaviors. One may require a specific amount of RAM, another may benefit from a GPU, and a third may benefit from executing on the same rack as a fourth. This paper promotes the need for and an approach for accommodating diverse tenant needs, based on having resource requests indicate any soft (i.e., when certain resource types would be better, but are not mandatory) and hard constraints in the form of composable utility functions. A scheduler that accepts such requests can then maximize overall utility, perhaps weighted by priorities, taking into account application specifics. Experiments with a prototype scheduler, called alsched, demonstrate that support for soft constraints is important for efficiency in multi-purpose clouds and that composable utility functions can provide it.