The Becue butt at 1-1/8" is the thinnest cue butt diameter I have found --- see below. Another European cue --- Shuriken Cues --- is virtually the same. The diameters below are for various cues and were collected from the following AZ posts:
Becue ______________________28.6 mm 1-1/8"
Shuriken Cues _____________28.9 mm or 1.14"
Viking skinny _____________ 30.6 mm
Predator Le4 ______________30.8 mm 1.211"
1980s Schon ______________31.0 mm 1.22"
Newer Predator|Blak 3-4 _ 31.2 & 31.4 mm
Pure X_____________________31.3 mm
Cuetec ____________________31.7 mm or 1.25"
1980s Schon ______________31.8 mm
Falcon ____________________32.0 mm
1980s Schon ______________32.3 mm 1.27"
2010 Predator ____________32.6 mm
Brunswick _________________32.7 mm
Mali ______________________ 32.8 mm
Meucci BMC ______________32.8 mm
Viking _____________________33 mm
Briggs (100-year old) _____35.3 mm
Brunswick Master Stroke _36.8 mm
WHP 22 ounce ___________37.5 mm