We conduct a discrete choice experiment on 1556 solo-driving commuters in Lyon, France to estimate the values of end-to-end travel time (VoTT) of commuting trips in the presence of a HOV-lane for four modes: Solo Driver, Carpool Driver, Carpool Passenger and Public Transport. Using discrete choice models, we find a strong heterogeneity in VoTT across modes and individuals. The analysis of individual heterogeneity distinguishes four behavior patterns: reluctant to mode change (20% of our sample), preferring the three alternative modes over solo driver (35%), preferring public transport (12%) and preferring driver modes whether solo or carpool (32%). We find that current solo drivers are more likely to switch to carpooling as a driver rather than as a passenger. As suggested by our simulations aimed at marginally changing mode shares, carpool passenger will be the scarce resource if one wants to decrease car traffic by stimulating carpooling for commuting trips.