Given a string $S$, we consider the problem of parsing it. Informally, an ``ideal parsing'' would provide: (i) ({\em Consistency in partition:}) Partition the string into short substrings of length $2$ or $3$ each, so that if identical substrings occur in different parts of $S$, then they are partitioned in the same way into short substrings. (ii) ({\em Consistency in labeling:}) Assign names to (or label) the short substrings so that identical short substrings get the same name, and thereby obtain a new string out of $S$. (iii) Apply items (i) and (ii) (recursively) to the new string. The talk will review a new technique for addressing the problem. A fundamental new idea in this work has been to use Cole-Vishkin's Deterministic Coin Tossing (DCT) technique to come close to ideal parsing. This has led to a novel and more efficient parallel algorithm for the key problem of suffix tree construction. Some more recent applications of that new technique will also be discussed. The use of DCT is intriguing, since its original introduction has been for a very different purpose: symmetry breaking in order to obtain more efficient parallel list ranking. (This work is joint with S.C. Sahinalp.)