  The phenomenon of quantum steering in bipartite quantum systems can be
reduced to the question whether or not the first party can perform measurements
such that the conditional states on the second party can be explained by a
local hidden state model. Clearly, the answer to this depends on the
measurements which the first party is able to perform. We introduce a local
hidden state model explaining the conditional states for all generalized
measurements on Bell-diagonal states of two qubits. More precisely, it is known
for the restricted case of projective measurements and Bell-diagonal states
characterised by the correlation matrix $T$ that a local hidden state model
exists if and only if $R_T= 2 \pi N_T |\det (T)| \ge 1$, where $N_T$ is defined
by an integral over the Bloch sphere. For generalized measurements described by
positive operator valued measures we construct a model if $R_T \ge 6/5$. Our
work paves the way for a systematic study of steerability of quantum states
with generalized measurements beyond the highly-symmetric Werner states.
