The methods used by Miller to construct his example has also been applied to get a modification of in [Charatonik 1979, Chapter IV, p. 230] (an outline of this construction is in [Caratonik 1977]). Below we summarize properties of this example, and recall an extension of this construction.

- There exists a dendrite such that:
- each point of is of order nor greater than ;
- for each the set of all points of which are of order is dense in ;
- is strongly rigid;
- is chaotic.

- For any two integers and with
there exists
a dendrite such that (see [Charatonik et al. 1996, Theorem 5.5, p. 185] and
compare also [Charatonik 1999, Theorem 27, p. 24]):
- for each .
- Every arc in contains a point of order in .
- Each of the sets: of all end points of , of all points of order in and of all points of order in is dense in .
- is strongly chaotic.

Dendrite is called a

*modified Miller dendrite*. (For a further modification of the above construction that leads to chaotic, strongly rigid, openly rigid and not strongly chaotic dendrites, see [Charatonik 2000, Theorem 3.14, p. 650].)Finally recall dendrites constructed in [Charatonik 1999, Examples 33 and 35, p. 28].

- For each natural , there exists a strongly rigid and not chaotic dendrite, all points of which are of order at most ([Charatonik 1999, Example 33, p. 28]).
- There exists a rigid dendrite which is neither chaotic nor strongly rigid ([Charatonik 1999, Example 35, p. 28]).