  We study covariant entropy bounds in dynamical spacetimes with naked
singularities. Specifically we study a spherically symmetric massless scalar
field solution. The solution is an inhomogeneous cosmology with an initial
spacelike singularity, and a naked timelike singularity at the origin. We
construct the entropy flux 4-vector for the scalar field, and show by explicit
computation that the generalized covariant bound $S_{L(B,B')}\le (A(B)-A(B'))/4
$ is violated for light sheets $L(B,B')$ in the neighbourhood of the (evolving)
apparent horizon. We find no violations of the Bousso bound (for which
$A(B')=0$), even though certain sufficient conditions for this bound do not
hold. This result therefore shows that these conditions are not necessary.
