  In this article we suggest a new approach to the systematic, computer-aided
construction and to the classification of product-quotient surfaces,
introducing a new invariant, the integer gamma, which depends only on the
singularities of the quotient model X=(C_1 x C_2)/G. It turns out that gamma is
related to the codimension of the subspace of H^{1,1} generated by algebraic
curves coming from the construction (i.e., the classes of the two fibers and
the Hirzebruch-Jung strings arising from the minimal resolution of
singularities of X).
  Profiting from this new insight we developped and implemented an algorithm
which constructs all regular product-quotient surfaces with given values of
gamma and geometric genus in the computer algebra program MAGMA. Being far
better than the previous algorithms, we are able to construct a substantial
number of new regular product-quotient surfaces of geometric genus zero. We
prove that only two of these are of general type, raising the number of known
families of product-quotient surfaces of general type with genus zero to 75.
This gives evidence to the conjecture that there is an effective bound of the
form gamma < Gamma(p_g,q).
