Neurophysiological studies of cognitive mechanisms such as visual attention typically ignore trial-by-trial variability and instead report mean differences averaged across many trials. Advances in electrophysiology allow for the simultaneous recording of small populations of neurons, which may obviate the need for averaging activity over trials. We recently introduced a method called the attention axis that uses multi-electrode recordings to provide estimates of attentional state of behaving monkeys on individual trials. Here, we refine this method to eliminate problems that can cause bias in estimates of attentional state in certain scenarios. We demonstrate the sources of these problems using simulations and propose an amendment to the previous formulation that provides superior performance in trial-by-trial assessments of attentional state.