It has been reported that narcoleptics exhibit deficits in short-term memory, list recall, and stimulus frequency estimation compared with control subjects. It is also well-known that pupil dilation during cognitive tasks is a measure of subject attention state. Here we present results from six narcoleptics and six controls, a total of 360 experimental records in which pupillograms were made during cognitive tests, which indicate that narcoleptics begin pupillary dilations at a smaller diameter, begin dilating earlier poststimulus, attain higher pupillary diameter velocities, yet achieve the same equilibrium dilation diameter as controls. These findings are derived from statistical tests performed on the parameters of a nonlinear regression model of pupillary cognitive dilation as a function of time. In our experiments, the standard 1-s interdigit time between cognitive stimuli was increased to 2.3 s, which yielded pupillographic time records showing that the process of short-term memory overload sets in gradually at about four memory digits for controls and three memory digits for narcoleptics. We suggest our results can be partially explained by a narcoleptic stimulus-encoding deficit, which limits the time available for subjects to rehearse cognitive tasks. However, we also report the unexpected finding that the inferred encoding deficit is a transient one in that repeated tasks at the same memory load elicit a near normal naroleptic pupillary dilation.