  We develop a new formalism for modeling the formation and evolution of
galaxies within a hierarchical universe. Similarly to standard semi-analytical
models we trace galaxies inside dark-matter merger-trees. The formalism
includes treatment of feedback, star-formation, cooling, smooth accretion, gas
stripping in satellite galaxies, and merger-induced star bursts. However,
unlike in other models, each process is assumed to have an efficiency which
depends only on the host halo mass and redshift. This allows us to describe the
various components of the model in a simple and transparent way. By allowing
the efficiencies to have any value for a given halo mass and redshift, we can
easily encompass a large range of scenarios. To demonstrate this point, we
examine several different galaxy formation models, which are all consistent
with the observational data. Each model is characterized by a different unique
feature: cold accretion in low mass haloes, zero feedback, stars formed only in
merger-induced bursts, and shutdown of star-formation after mergers. Using
these models we are able to examine the degeneracy inherent in galaxy formation
models, and look for observational data that will help to break this
degeneracy. We show that the full distribution of star-formation rates in a
given stellar mass bin is promising in constraining the models. We compare our
approach in detail to the semi-analytical model of De Lucia & Blaizot. It is
shown that our formalism is able to produce a very similar population of
galaxies once the same median efficiencies per halo mass and redshift are being
used. We provide a public version of the model galaxies on our web-page, along
with a tool for running models with user-defined parameters. Our model is able
to provide results for a 62.5 h^{-1} Mpc box within just a few seconds.
