Existing theoretical evidence on optimal currency spacing is fragmenta
ry and, to some extent, contradictory. This note brings together the p
ieces and tries to solve the puzzle. It shows that if the spacing of d
enominations is uniform, then the average number of notes and coins ex
changed in a transaction can be minimized by spacing denominations apa
rt by a factor of two, even when allowing for overpayment and the retu
rn of change.