The nipping loops of those TIB bowlines ( tied with the simple, easy and quick "haltering collar" method, described at the previous posts ) encircle
two, only, rope diameters - and this may be a disadvantage (

) : a wider, rounder nipping turn, encircling
three rope diameters, is probably a stronger and certainly a better-looking nipping structure. Also, in the cases of "secure", two-collar ( = double collar ) bowlines, the fact that the divided-by-three gripping power of a "wide" nipping loop is smaller than a divided-by-two "narrow" one, is not important - because, regarding the defence against the slippage of the Tail End,
a more complex, double collar structure is always much more efficient than a more tight single, or a more complex double nipping structure . Contrary to one more of the many "popular" knotting myths,
a double-collar bowline is always more secure than a double-nipping-loop one. It is always more beneficial to force the slipping Tail End to make one more 180-degrees U-turn ( as it happens in the case of the "Janus" bowline(s)), than to nip it a second time, on a second point, inside a second nipping loop ( as it happens in the case of the "Double" and of the "Water" bowline ).
There is very easy way, in the eye-knots tied with the help of this method, to dispense with the "narrow" nipping loop disadvantage, but retain the TIB advantage : we have only to
transform the TIB bowlines to TIB crossing-knot based loops, as shown in this post. In those loops, the "haltering collar" is not tied on the returning eye leg, but on the Standing Part, before the eye ( see the attached picture, and compare it to the picture at Reply#13 ). And the fact that, by this transformation, the double nipping structure, tied on the Standing Part, becomes a double collar structure, tied on the returning eye leg, means that
the first curve encircles two rope diameters - so, compared to what happens in the majority of the crossing-knot based eye-knots, this curve is now much smoother and wider.
I believe that the crossing-knot based loops have not attracted the attention of the knot tyers they deserve : their nipping structures are very stable and well-balanced, and they can remain "closed" without exploiting the integrity of the collar structures too much. Moreover, if they are arranged to be wrapped around
double collar structures ( as the Girth hitch shown in the attached picture ), they distribute the high tensile forces coming from the Standing End to more segments, across a more extended area of the nub, so they may lead to not only very secure, but very strong eye-knots as well.