We present high-resolution (R similar to 170,000) Kitt Peak National Observ
atory coude feed telescope observations of the interstellar K I lambda 7698
line toward five multiple star systems with saturated Na I components. We
compare the K I absorption-line profiles in each of the two (or three) line
s of sight in these systems and find significant differences between the si
ght lines in three out of the five cases. We infer that the small-scale str
ucture traced by previous Na I observations is also present in at least som
e of the components with saturated Na I absorption lines, and thus the smal
l-scale structures traced by the neutral species are occurring at some leve
l in clouds of all column densities. We discuss the implications of that co
nclusion and a potential explanation by density inhomogeneities.