  We present a new approach for determining spatially optimized operators that
can be used for lattice spectroscopy of excited hadrons. Jacobi smeared quark
sources with different widths are combined to construct hadron operators with
different spatial wave functions. We use the variational method to determine
those linear combinations of operators that have optimal overlap with ground
and excited states. The details of the new approach are discussed and we
demonstrate the power of the method using examples from quenched baryon and
meson spectroscopy. In particular we study the Roper state and rho(1450) and
discuss some physical implications of our tests.
