Three simple improvements are presented which, for a given accuracy, result in a 10-20-fold decrease in computation time for simulation of arbitrarily branched active cables with Hodgkin Huxley (HH) kinetics. The first improvement takes advantage of the essentially tridiagonal character of the matrix equation for each branch of a 'tree' network and solves the equations as efficiently as for an unbranched cable. The second improvement evaluates the HH membrane conductances at the midpoint of a time step, delta t, to maintain full second order accuracy, 0(delta t2), with no increase in the number of computational steps. The third improvement makes use of 'premultiplied' HH rate function tables for very efficient second order correct integration of HH membrane conductance.