nk/logn) lower bound for deterministic token-forwarding algorithms that are not allowed to combine, split, or change tokens in any way. In the present paper, we extend this bound in different ways. If nodes are allowed to forward b?≤-em class="a-plus-plus">k tokens instead of only one token in every round, a straight-forward extension of the O(nk) algorithm disseminates all k tokens in time O(nk/b). We show that for any randomized token-forwarding algorithm, Ω(n--em class="a-plus-plus">nk/(b 2lognloglogn)) rounds are necessary. If nodes can only send a single token per round, but we are guaranteed that the network graph is c-vertex connected in every round, we show a lower bound of Ω(nk/(clog3/2 n)), which almost matches the currently best O(nk/c) upper bound. Further, if the network is T-interval connected, a notion that captures connection stability over time, we prove that Ω(n--em class="a-plus-plus">nk/(T 2logn)) rounds are needed. The best known upper bound in this case manages to solve the problem in O(n--em class="a-plus-plus">nk/T) rounds. Finally, we show that even if each node only needs to obtain a δ-fraction of all the tokens for some δ?∈?[0,1], Ω(nkδ 3/logn) are still required." />