In a partially ordered set P, let a pair of elements (x,y) be called alpha-balanced if the proportion of linear extensions that has x before y is between alpha and 1-alpha. The 1/3-2/3 Conjecture states that every finite poset which is not a chain has some 1/3-balanced pair. While the conjecture remains unsolved, we extend the list of posets that satisfy the conjecture by adding certain lattices, including products of two chains, as well as posets that correspond to Young diagrams.