Will jams get worse when slow cars move over?

Motivated by an analogy with traffic, we simulate two species of particles (`vehicles'), moving stochastically in opposite directions on a two-lane road. In this simple modification of the asymmetric exclusion process, each species prefers one lane over the other, controlled by a parameter $0 \leq b \leq 1$ such that $b=0$ corresponds to random lane choice and $b=1$ to perfect `laning'. We find that the system displays one large cluster (`jam') whose size increases with $b$, contrary to intuition. Even more remarkably, the lane `charge' (a measure for the number of particles in their preferred lane) exhibits a region of negative response: even though vehicles experience a stronger preference for the `right' lane, more of them find themselves in the `wrong' one! For $b$ very close to $1$, a sharp transition restores a homogeneous state. Various characteristics of the system are computed analytically, in good agreement with simulation data.