When chaining compressions with image, like "dsk.foo.bar", the original command for 'foo' gets run again. This is easily observable by defining following dummy commands:

COMPRESSIONTYPES_append = " dummy"
COMPRESS_CMD_dummy = "echo 'running dummy command' && touch ${IMAGE_NAME}.${type}.dummy"

COMPRESSIONTYPES_append = " anotherdummy"
COMPRESS_CMD_anotherdummy = " echo 'Another dummy command'"

and defining compression like "dsk.dummy.anotherdummy"

When building the image, the log file will now contain the following lines:

running dummy command
running dummy command
Another dummy command


Bitbake version:

$ bitbake --version
BitBake Build Tool Core version 1.30.0