  We work out the truncation from maximal to half-maximal supergravity in four
dimensions. In particular, we determine the explicit constraints on the
embedding tensors of both theories. These tensors specify the complete
theories, including gauge groups and scalar potentials. Firstly, we find the
linear constraint on N=8 theories to allow for a truncation to N=4. Secondly,
we determine the additional N=4 quadratic constraints following from N=8.
Finally, we comment on a brane interpretation as tadpole conditions for the
latter.
