We consider scalar Bose fields Φ in 1+1 dimensions which are bounded [i.e., Φ(F) is a bounded operator], commute for space- and timelike distances, and are dilation covariant with scaling dimension d=1,3,5,… . We show that their truncated n-point-functions WnT are related to the truncated functions VnT of φ(x)=ψd/2(x+)⊗ψd/2(x−) via WnT=cnVnT with cn>0. ψd/2(x±) is a free chiral real Fermi field of dimension d/2 depending on the light cone coordinates x±=t±x. This comes close to the conjecture that under the above assumptions Φ is nothing but a weighted s-product of φ=ψd/2⊗ψd/2.