We present a detailed experimental investigation of the easy-hard-easy phase transition for randomly generated instances of satisfiability problems. Problems in the hard part of the phase transition have been extensively used for benchmarking satisfiability algorithms. This study demonstrates that problem classes and regions of the phase transition previously thought to be easy can sometimes be orders of magnitude more difficult than the worst problems in problem classes and regions of the phase transition considered hard. These difficult problems are either hard unsatisfiable problems or are satisfiable problems which give a hard unsatisfiable subproblem following a wrong split. Whilst these hard unsatisfiable problems may have short proofs, these appear to be difficult to find, and other proofs are long and hard. * The first author was supported by a SERC Postdoctoral Fellowship and the second by a HCM Postdoctoral fellowship. We thank Alan Bundy, Bob Constable, Pierre Lescanne, Paul Purdom, the members of the Mathematical Reasoning Group at Edinburgh, the Eureca group at INRIA-Lorraine, and the Department of Computer Science at Cornell University for their constructive comments and for rather a lot of CPU cycles. We also wish to thank our anonymous referees who suggested several important improvements to this paper.