Impulse propagation in small-diameter (1–3 μm) axons with inhomogeneous geometry was simulated. The fibres were represented by a series of 3 μm-long compartments. The cable equation was solved for each compartment by a finite-difference approximation (Cooley and Dodge 1966). First-order differential equations governing temporal changes in membrane potential or Hodgkin-Huxley (1952) conductance parameters were solved by numerical integration. It was assumed that varicosity and intervaricosity segments had the same specific cable constants and excitability properties, and differed only in length and diameter. A single long varicosity or a ‘clump’ of 3 μm-long varicosities changed the point-to-point (axial) conduction velocity within as well as to either side of the geometrically inhomogeneous regions. When 2 μm-diameter, 3 μm-long varicosities were distributed over the 1 μm-diameter fiber length as observed in serotonergic axons, mean axial conduction velocity was between that of uniform-diameter 1 and 2 μm fibers, and changed predictably with different cable parameters. Fibers with inexcitable varicosity membranes also supported impulse propagation. These simulations provided a general theoretical basis for the slow (< 1 M/s) conduction velocity attributed to small-diameter unmyelinated varicose axons.