We present a full band Monte Carlo algorithm based on phase-space simp
lexes which has all of the advantages of analytical band Monte Carlo w
hile preserving the accuracy of a full band structure. An adaptive, co
ntour-aligned grid represents the energy band structure within the irr
educible wedge to within an arbitrary tolerance. This discretization a
llows exact treatment of the equations of motion and final state selec
tion for a wide class of scattering mechanisms. Results using this met
hod show at least an order of magnitude improvement in performance ove
r previous full band codes.