We present efficient algorithms for two all-to-all communica- tion operations in message-passing systems: inder (or all-to- all personalized communication) and concatenation (or all- to-all broadcast). We assume a model of a fully-connected message-passing system, in which the performance of any point-to-point communication is independent of the sender- receiver pair. We also assume that each processor has k≥ 1 ports, through which it can send and receive k messages in every communication round. The complexity measures we use are independent of the particular system topology and are based on the communication start-up time and on the communication bandwidth. In the index operation among n processors, initially, each processor has n blocks of data, and the goal is to exchange the i-th block of processor j with the j-th block of processor i. We present a class of index algorithms that is designed for all values of n and that features a trade-off between the com- munication start-up time and the data transfer time. This class of algorithms includes two special cases: an algorithm that is optimal with respect to the measure of the start-up time, and an algorithm that is optimal with respect to the measure of the data transfer time. We also present exper- imental results featuring the performance tuneabilty of our index algorithms on the IBM SP-1 parallel system. In the concatenation operation among n processors, ini- tially, each processor has one block of data, and the goal is to concatenate the n blocks of data from the n proces- sors and to make the concatenation result known to all the processors. We present a concatenation algorithm that optimal, for most values of n, in the number of communica- tion rounds and in the amount of data transferred.