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The rates at which a user can generate device-independent quantum randomnumbers from a Bell-type experiment depend on the measurements that heperforms. By numerically optimising over these measurements, we present lowerbounds on the randomness generation rates for a family of two-qubit statescomposed from a mixture of partially entangled states and the completely mixedstate. We also report on the randomness generation rates from a tomographicmeasurement. Interestingly in this case, the randomness generation rates arenot monotonic functions of entanglement.

Maximizing device-independent randomness from a Bell experiment by optimizing the measurement settings