  We develop a method to efficiently calculate trial wave functions for quantum
Hall systems which involve projection onto the lowest Landau level. The method
essentially replaces lowest Landau level projection by projection onto the $M$
lowest eigenstates of a suitably chosen hamiltonian acting within the lowest
Landau level. The resulting "energy projection" is a controlled approximation
to the exact lowest Landau level projection which improves with increasing $M$.
It allows us to study projected trial wave functions for system sizes close to
the maximal sizes that can be reached by exact diagonalization and can be
straightforwardly applied in any geometry. As a first application and test
case, we study a class of trial wave functions first proposed by Girvin and
Jach, which are modifications of the Laughlin states involving a single real
parameter. While these modified Laughlin states probably represent the same
universality class exemplified by the Laughlin wave functions, we show by
extensive numerical work for systems on the sphere and torus that they provide
a significant improvement of the variational energy, overlap with the exact
wave function and properties of the entanglement spectrum.
