Packing a Delivery via function modules or BAPI's

Does anyone know the correct function modules to call in order to pack an outbound delivery. The HU is already been entered into the delivery. I just need to pack all the items into this HU and PGI the delivery. I've tried the following function modules:

SD_DELIVERY_UPDATE_PACKING

V51P_FIND_HEADER

V51P_NEUE_HU_PRO

I'm not sure what I'm doing wrong but the delivery doesn't get packed. Anyone have a clue?

Thank you,