  We propose a very general construction of simple Virasoro modules
generalizing and including both highest weight and Whittaker modules. This
reduces the problem of classification of simple Virasoro modules which are
locally finite over a positive part to classification of simple modules over a
family of finite dimensional solvable Lie algebras. For one of these algebras
all simple modules are classified by R. Block and we extend this classification
to the next member of the family. As a result we recover many known but also
construct a lot of new simple Virasoro modules. We also propose a revision of
the setup for study of Whittaker modules.
