For n = 0, 1 and 2, we define an n-motivic t-structure on Voevodsky's triangulated category of effective motives. The 0-motivic t-structure is taken to be the homotopy t-structure, but for n = 1 and 2, we get new t-structures. We show that the heart of the 1-motivic t-structure contains the category of Deligne's 1-motives. We then specify certain objects in the heart of the 2-motivic t-structure which we call mixed 2-motives. We also show that the category of mixed 2-motives is abelian.