I bought a 3 legged thing just before Christmas from Jessops - A Leo with an Airhed Switch ball head - My Manfrotto tripod was too heavy for general travel around, and so was looking for something compact, lightweight, would fit in a suitcase, be easy to carry around but still hold a Canon 1dx2. My choice was this:
https://3leggedthing.com/leo
It folds down to 34cm without the head - and with the head is well within your requirements.
So far my thoughts are:
Pros:
Light
Easy to carry
Lots of different positions available - I like the ability to mount the camera upside down under the tripod - so the camera is literally a mm off the ground.
Ball head is quite reasonable
Holds my 1dx2 with primes easily and steadily
Cons
I find the finish a little easy to scratch - so it's being used as a working machine - but I can see it not looking so pretty in a year's time.
Due to it being so compact - and extending to such a length - it's necessary to have a lot of twisty connections. Can be a little time consuming putting it up and down - but I've kinda got used to that now.
Shakes a little when I press the shutter with my 1dx2 and 70-200mm 2.8 - but with the use of a self timer I'm able to manage that
Overall - it allows me to carry a tripod when I travel without too much of a headache. It has a few weak areas - but overall does the job well.
https://a.uguu.se/n7eHcLTSiq2c_519e81b791794305a9cb2cf6e6b3e219.MOV
Here you can see it in action when I used it in HK last week - it's one of those 24h temporary video hostings - so be quick to watch it