  We show that three unsharp binary qubit measurements are enough to violate a
generalized noncontextuality inequality, the LSW inequality, in a
state-dependent manner. For the case of trine spin axes we calculate the
optimal quantum violation of this inequality. Besides, we show that unsharp
qubit measurements do not allow a state-independent violation of this
inequality. We thus provide a minimal state-dependent proof of measurement
contextuality requiring one qubit and three unsharp measurements. Our result
rules out generalized noncontextual models of these measurements which were
previously conjectured to exist. More importantly, this class of generalized
noncontextual models includes the traditional Kochen-Specker (KS) noncontextual
models as a proper subset, so our result rules out a larger class of models
than those ruled out by a violation of the corresponding KS-inequality in this
scenario.
