  The Bisognano-Wichmann property for local, Poincar\'e covariant nets of
standard subspaces is discussed. We present a sufficient algebraic condition on
the covariant representation ensuring Bisognano-Wichmann and Duality properties
without further assumptions on the net. Our modularity condition holds for
direct integrals of scalar massive and massless representations. We conclude
that in these cases the Bisognano-Wichmann property is much weaker than the
Split property. Furthermore, we present a class of massive modular covariant
nets not satisfying the Bisognano-Wichmann property.
