  We study $\ell^2$ Betti numbers, coherence, and virtual fibring of random
groups in the few-relator model. In particular, random groups with negative
Euler characteristic are coherent, have $\ell^2$ homology concentrated in
dimension 1, and embed in a virtually free-by-cyclic group with high
probability. Similar results are shown with positive probability in the zero
Euler characteristic case.
