Intermediate-resolution (60 00 less than or equal to R less than or equal t
o 120 000) observations of interstellar Na I lines towards 29 stars in the
general direction of the Lupus molecular clouds (330 degrees less than or s
imilar to l less than or similar to 350 degrees; 0 degrees less than or sim
ilar to b less than or similar to 25 degrees) are presented. Previously pub
lished spectra towards an additional seven stars are also included. Based o
n the Hipparcos distances to these stars, and the minimum distance at which
strong interstellar Na I lines appear in the spectra, I obtain a distance
of similar to 150 +/- 10 pc to the Lupus molecular complex. While in agreem
ent with a number of other independent estimates, this result is at odds wi
th the value of 100 pc recently obtained by Knude & Hog from a Hipparcos-ba
sed study of interstellar extinction. A possible explanation for this discr
epancy is discussed, and it is concluded that the value of 150 +/- 10 pc ob
tained here is to be preferred. In addition, these observations have some o
ther implications for the structure of the interstellar medium in this dire
ction, and these are briefly considered.