  We design and fabricate ultra-low-loss tapered optical fibers (TOFs) with
minimal lengths. We first optimize variations of the torch scan length using
the flame-brush method for fabricating TOFs with taper angles that satisfy the
adiabaticity criteria. We accordingly fabricate TOFs with optimal shapes and
compare their transmission to TOFs with a constant taper angle and TOFs with an
exponential shape. The highest transmission measured for TOFs with an optimal
shape is in excess of 99.7 % with a total TOF length of only 23 mm, whereas
TOFs with a constant taper angle of 2 mrad reach 99.6 % transmission for a 63
mm TOF length.
