  We investigate the behavior of the superconducting transition temperature
within a previously developed BCS-Bose Einstein crossover picture. This
picture, based on a decoupling scheme of Kadanoff and Martin, further extended
by Patton, can be used to derive a simple form for the superconducting
transition temperature in the presence of a pseudogap. We extend previous work
which addressed the case of s-wave pairing in jellium, to explore the solutions
for T_c as a function of variable coupling in more physically relevant
situations. We thereby ascertain the effects of reduced dimensionality,
periodic lattices and a d-wave pairing interaction. Implications for the
cuprate superconductors are discussed.
