Free energy barrier and mean translocation time, tau, are calculated for the movement of a single Gaussian chain from one sphere to another larger sphere through a narrow pore. The potential interaction between the polymer and pore significantly modifies the entropic barrier landscape of translocation. As the pore length increases, the translocation process undergoes a transition from entropic barrier mechanism to a mechanism dominated by the pore-polymer interaction. This shift in mechanism leads to nonmonotonic dependence of tau on the pore length. Explicit formulas are derived for the dependence of tau on chain length, pore length, sizes of the donor and recipient spheres, strength of pore-polymer interaction, applied voltage, and electrochemical potential gradient for translocation. The calculated results provide guidance for tuning the rate of polymer translocation through narrow pores. (C) 2003 American Institute of Physics.