LSQR uses the Golub-Kahan bidiagonalization process to solve sparse least-squares problems with and without regularization. In some cases, projections of the right-hand side vector are required, rather than the least-squares solution itself. We show that projections may be obtained from the bidiagonalization as linear combinations of (the-oretically) orthogonal vectors. Even the least-squares solution may be obtained from orthogonal vectors, perhaps more accurately than the usual LSQR solution. (However, LSQR has proved equally good in all examples so far.)