We consider the Oseen system with resolvent term in an exterior domain in R3, supplemented by homogeneous Dirichlet boundary conditions. Under the assumption that the resolvent parameter λ is close to zero and ℜλ≥0, λ≠0, we estimate the Lp-norm of the velocity against the Lp-norm of the right-hand side, times a factor C|λ|−2, with C>0 independent of λ. Such an estimate cannot hold for this range of λ if |λ|−2 is replaced by |λ|−κ with κ<3/2, and there are indications that κ∈[3/2,2) cannot be admitted either. We present various other Lp-estimates of Oseen resolvent flows for the same range of λ. Our article is complementary to the work by T. Kobayashi and Y. Shibata (1998) [20], where Oseen resolvent estimates are derived under the assumption that |λ|≥c0, for some arbitrary but fixed c0>0, with the constant in the resolvent estimate depending on c0.