I will describe a construction of symplectic manifolds diffeomorphic to T^* S^n, but with symplectic structure different from the canonical one. The construction uses symplectic Lefschetz fibrations, which give a flexible way to build open symplectic manifolds. The resulting manifolds are well-adapted to tools from Floer theory, which sometimes allows us to distinguish them from each other. I will try to roughly explain what all these words mean and how the construction works.