Managing compression based on a compression profile of host data initially residing on a source storage array

A technique manages compression based on host data initially residing on a source storage array. The technique involves providing, based on source segments of the host data while the host data initially resides on the source storage array, compressibility labels (or tags) that label the source segments of the host data. Each compressibility label indicates a projected compression level for a respective source segment of the host data. The technique further involves generating a compression profile based on the compressibility labels that label the source segments of the host data. The technique further involves providing, based on the compression profile, a compression tier configuration that defines a prearrangement of compression tiers on a target storage array that receives the host data from the source storage array, the prearrangement of compression tiers providing storage units of allocation having different predefined sizes.