The problem of electronic energy transfer in a network of two-level systems coupled to a single trapping site is investigated using a simple Haken-Strobl model with diagonal disorder. The goal is to illustrate how the trapping time T-trap, coherence time T-d, and molecular topology all affect the overall efficiency of a light-harvesting network. Several issues are identified that need to be considered in the design of an optimal energy transfer network, including the dephasing-induced decoupling the trap from the rest of the network, the nonlinear dependence of trapping rate on the coherence time, and the role of network size and connectivity in determining the effect of the coherence time on efficiency. There are two main conclusions from this work. First, there exists an optimum combination of trapping time and coherence time, which will give the most rapid population transfer to the trap. These values are not in general the shortest trapping time and the longest coherence time, as would be expected based on rate equation models and/or simple considerations from previous analytical results derived for the Haken-Strobl model in an infinite system. Second, in the coherent regime, where T-d is longer than the other relevant timescales, population trapping in a finite system can be suppressed by quantum interference effects, whose magnitude is sensitive to the molecular geometry. Suggestions for possible methods of observing such effects are discussed. These results provide a qualitative framework for quantum coherence and molecular topology into account for the design of covalent light-harvesting networks with high energy transfer efficiencies. (C) 2004 American Institute of Physics.