Abstract: We revisit certain problems of pose estimation based on 3D--2D correspondences between features which may be points or lines. Specifically, we address the two previously-studied minimal problems of estimating camera extrinsics from $p \in \{ 1, 2 \}$ point--point correspondences and $l=3-p$ line--line correspondences. To the best of our knowledge, all of the previously-known practical solutions to these problems required computing the roots of degree $\ge 4$ (univariate) polynomials when $p=2$, or degree $\ge 8$ polynomials when $p=1.$ We describe and implement two elementary solutions which reduce the degrees of the needed polynomials from $4$ to $2$ and from $8$ to $4$, respectively. We show experimentally that the resulting solvers are numerically stable and fast: when compared to the previous state-of-the art, we obtain nearly an order of magnitude speedup.