  In this paper, we propose a generalization for the class of laura algebras,
which we call almost laura. We show that this new class of algebras retains
most of the essential features of laura algebras, especially concerning the
important role played by the non-semiregular components in their
Auslander-Reiten quivers. Also, we study more intensively the left supported
almost laura algebras, showing that these are characterized by the presence of
a generalized standard, convex and faithful component. Finally, we prove that
almost laura algebras behave well with respect to full subcategories,
split-by-nilpotent extensions and skew group algebras.
