The assumption that (M2m+ 1, φ, ξ, η, g) is a contact metric manifold is very weak, since the set of metrics associated to the contact form η is huge. Even if the structure is^-Einstein we do not have a complete classification. Also for m= l, we know very little about the geometry of these manifolds [8]. On the other hand if the structure is Sasakian, the Ricci operator Q commutes with ψ ([!]> P 76), but in general QφΦφQ and the problem of the characterization of contact metric manifolds with Qφ—φQ is open. In£ 13] Tanno defined a special family of contact metric manifolds by the requirement that ξ belong to the^-nullity distribution of g. We also know very little about these manifolds (see [13] and [9]). In § 3 of this paper we first prove that on a 3-dimensional contact metric manifold the conditions, i) the structure is^-Einstein, ii) Qφ—φQ and iii) ξ belongs to the^-nullity distribution of g are equivalent. We then show that a 3-dimensional contact metric manifold on which Qφ—φQ is either Sasakian, flat or of constant ξ-sectional curvature k and constant^-sectional curvature—k. Finally we give some auxiliary results on locally^-symmetric contact metric 3-manifolds and on contact metric 3-manifolds immersed in a 4-dimensional manifold of contant curvature+ 1.