  Unsharp measurements are widely seen as the key resource for recycling the
nonlocality of an entangled state shared between several sequential observers.
Contrasting this, we here show that nonlocality can be recycled using only
standard projective measurements, without using quantum ancillas. Focusing on
the CHSH inequality, we determine the optimal trade-off in the Bell parameters
for a maximally entangled two-qubit state in the presence of shared classical
randomness. We then find that non-maximally entangled states make possible
larger sequential violations, which contrasts the standard CHSH scenario.
Furthermore, we show that nonlocality can be recycled even when only using
projective measurements and local randomness. We discuss the implications of
our results for experimental implementations of sequential nonlocality.
