  We study the bilateral trade problem where a seller owns a single indivisible
item, and a potential buyer seeks to purchase it. Previous mechanisms for this
problem only considered the case where the values of the buyer and the seller
are drawn from independent distributions. In this paper, we study bilateral
trade mechanisms when the values are drawn from a joint distribution.
  We prove that the buyer-offering mechanism guarantees an approximation ratio
of $\frac e {e-1} \approx 1.582$ to the social welfare even if the values are
drawn from a joint distribution. The buyer-offering mechanism is Bayesian
incentive compatible, but the seller has a dominant strategy. We prove the
buyer-offering mechanism is optimal in the sense that no Bayesian mechanism
where one of the players has a dominant strategy can obtain an approximation
ratio better than $\frac e {e-1}$. We also show that no mechanism in which both
sides have a dominant strategy can provide any constant approximation to the
social welfare when the values are drawn from a joint distribution.
  Finally, we prove some impossibility results on the power of general Bayesian
incentive compatible mechanisms. In particular, we show that no deterministic
Bayesian incentive-compatible mechanism can provide an approximation ratio
better than $1+\frac {\ln 2} 2\approx 1.346$.
