Recently, attempts have been made to separate the problem of parallel sorting from that of list ranking, in order to get around the well known\Omega\Gamma/33 n= log log n) lower bound. These approaches have been of two kinds - chain sorting and padded sorting. Here we present nearly optimal, comparison based padded sorting algorithms that run in average case time O( 1 ffl 2 + 1 ffl log log n) using n 1+ffl processors, and O(n 1+ffl ) space, on an Common CRCW PRAM.From these results, algorithms for chain sorting within the same time and processor bounds can be easily obtained. Using a similar approach, we also give an O(1) average case time, comparison based algorithm for finding the largest of n items using a linear number of processors. The algorithm for finding the maximum, runs on a Common CRCW PRAM using only n 3=4 cells of shared memory. Finally, we obtain randomised algorithms for these problems that run on Common/Tolerant CRCW PRAMs, and also satisfy the above...