Atomic-scale computer simulations can be used to predict, explain, and improve the performance of prospective nanoscale transistors and devices, which are key components in modern electronics. In particular, first-principles simulations of electronic transport can predict the conductance of atomic-scale materials by computing the quantum mechanical probability for electrons to move through the material. To simulate open boundary conditions in a finite simulation cell, the electronic transport code TRANSEC uses complex-valued functions known as complex absorbing potentials (CAPs), which simulate electrons flowing into and out of the simulation cell, thereby preventing reflection of electrons from the cell boundaries. The effectiveness of CAPs depends on CAP parameters, such as CAP strength and width, which must be tuned for a given material. In general, wider CAPs usually absorb better, but require more space to accommodate the CAPs themselves, increasing the simulation’s size and hence computing time. The goal of our research has been to optimize the CAP form and volume so as to reduce the CAP’s impact on computing time. We have evaluated CAP forms and widths using a simplified tight-binding model of an electronic transport calculation. Our results indicate that an order 1.8 monomial CAP is a highly efficient CAP form, and appears to compare favorably against previously used Gaussian CAPs. Our finding of the optimal monomial range is in broad agreement with previous findings of Seideman & Miller [J. Chem. Phys. 96, 4412]. We have also reproduced these results with TRANSEC, showing that monomial CAPs of monomial order between 1.5 and 2.0 may absorb electrons effectively even for a narrow CAP width, potentially reducing computing time by 25% to 50%. We have confirmed that monomial CAPs of order 1.8 can be tuned successfully for several different nanoscale structures, and can reduce computing time.