In a recently proposed parallel execution model, operators as well as data operands are dynamically generated at execution time, and enter a special matching store which must accommodate either operator or operands arriving first in time. Here, we extend this execution model to permit the compiler to adjust the granularity of scheduled units emerging from the matching store, a problem which is complicated by the increased dynamics of the proposed execution model. Compiler output code is described in detail. Effects of different fragmentations on program speed and resource requirements are examined, using architectural simulations for a number of application programs compiled using different fragmentation methods. Architectural implications are discussed.