The Half-Mess is a variation of
Mills Mess in which the last ball of the cycle is made as an overthrow,
instead of the standard under-the-arm throw. This leads to an asymmetrical
pattern in which one particular hand is always crossing over the other after
Technically, the Half-Mess is an easier pattern than the full Mills Mess. However, since most people only hear about this pattern after they have already learned Mills Mess, it is easier to teach the Half-Mess as simply a modification of the normal pattern. Start by juggling Mills Mess, and then take the last ball of a cycle that will be caught by your dominant hand, and make an overthrow instead of crossing your arms. Afterwards, resume juggling Mills Mess.
As shown, practice this on both sides. To run the full Half-Mess, simply continue making that same overthrow each for each cycle. Once you master the Half-Mess in one direction, you can change which hand makes the overthrows and learn it in the opposite orientation.