We consider a model describing the one-dimensional confinement of an e
xciton in a symmetrical, rectangular quantum-well structure, and deriv
e upper and lower bounds for the binding energy E-b Of the exciton. Ba
sed on these bounds, we study the dependence of E-b On the width of th
e confining potential with a higher accuracy than previous reports. Fo
r an infinitely deep potential the binding energy varies, as expected,
from 1 exciton Rydberg R at large widths to 4 R at small widths. For
a finite potential, but without consideration of a mass mismatch or a
dielectric mismatch, we substantiate earlier results that the binding
energy approaches the value 1 R for both small and large widths, havin
g a characteristic peak for some intermediate size of the slab. Taking
the mismatch into account, this result will in general no longer be t
rue. For the specific case of a Ga1-xAlxAs/GaAs/Ga1-xAlxAs quantum-wel
l structure, however, and in contrast to previous findings, the peak s
tructure is shown to survive. [S0163-1829(98)08639-1].