In this paper, we define a new flavour of well-composedness, called strong Euler well-composedness. In the general setting of regular cell complexes, a regular cell complex of dimension n is strongly Euler well-composed if the Euler characteristic of the link of each boundary cell is 1, which is the Euler characteristic of an $$(n-1)$$
(
n
-
1
)
-dimensional ball. Working in the particular setting of cubical complexes canonically associated with $$n$$
n
D pictures, we formally prove in this paper that strong Euler well-composedness implies digital well-composedness in any dimension $$n\ge 2$$
n
≥
2
and that the converse is not true when $$n\ge 4$$
n
≥
4
.