New for: D1, D2, D3, D4, D5
and polynomially bad expansion profile. We show that, with high probability {\sf Push-Pull} propagates the rumor in O(log^2 n) rounds to almost all modes. Also we prove that with probability $1-o(1)$ the protocol needs at least n^{\Omega(1)} rounds to inform all nodes. This exponential dichotomy between time required for informing \emph{almost all} and \emph{all} nodes is striking.