  Answering a question of Harrington, we show that there exists a proper
forcing notion, which adds a minimal real $\eta \in \prod_{i<\omega} n^*_i$,
which is eventually different from any old real in $\prod_{i<\omega} n^*_i$,
where the sequence $\langle n^*_i \mid i<\omega \rangle$ grows slowly.
