When selecting a head, one wants to pair the legs with a head that will not compromise the stiffness of the system as a whole.  On the other hand, a head that is too big adds diminishing performance increases and just adds weight.  

Below is the optimization result for selecting a ball head.  This chart plots the stiffness to weight ratio for this tripod and each ball head that I have tested in blue dots versus the stiffness of those heads.  The red line is a generalized model for a strong performing ball head. The higher up on the this graph the higher stiffness/weight performance of the system.  More information on this analysis can be found in the ball head choice optimization page.

This chart is telling us that to optimize the stiffness to weight ratio for the system, we want to be choosing a good ball head of stiffness around 4000 Nm/rad or above.  This is right in the middle of what we considered to be mid-sized ball heads weighing around 1 lb, (~0.45 kg).  

Recommended Heads

Note that these recommendations are limited to the tripod heads I have tested.  The more general discussion above should provide adequate guidance if your head of choice is not listed.

FLM CB-38FTR – I haven’t tested the FLM CB-38, but have tested its larger brother the FLM CB-58FTR.  The design and construction of this line of heads is excellent, and the CB-38 will be the best size to pair with the CP30-S4 II legs.

Acratech GP – While the Acratech GP is often not quite stiff enough for the larger all-purpose tripods, it is a great match for this one.  Its strength to weight ratio isn’t as good as the others on this list, but its open design provides the best resistance to dirt and sand.

Really Right Stuff BH-40 – This is my personal favorite head to use with the CP30-S4.  Aside from having the extremely high build quality RRS is know for, the BH-40 is fairly short compared to the other heads on this list.  This allows the camera to stay lower and closer to the tripod’s apex and reduces the overall folded leng

Markins Q10i – The Markins heads have shown some of the best stiffness to weight ratios I have seen along with excellent build quality and mechanics.  If eking out every last bit of stiffness performance is your goal, this is the head for you.

Sirui K-30X – The Sirui K series provide excellent performance at an excellent price.  The K-30X is the appropriate size here.  This is by far the least expensive head on this list, but is still a high quality piece.  If the price of the legs was already pushing your budget, this head is a great place to help reign in the spending.

It is hard to wrong with any of the above ball heads.  Choose the one that best meets your needs.

The table below shows the estimated combined stiffness of this tripod with each head I have tested to date.  The plot above is simply a visual representation of the last two columns in this table.  The recommended heads are loosely based off this list but take into account other subjective factors of ergonomics, build quality, and value.