Model-checkers are powerful tools that can find individual traces through models to satisfy desired properties. These traces provide solutions to a number of problems. Instead of individual traces, software testing needs sets of traces that satisfy coverage criteria. Finding a trace set in a large model is difficult because model checkers generate single traces and use a lot of memory. Space and time requirements of model-checking algorithms grow exponentially with respect to the number of variables and parallel automata of the model being analyzed. We present a method that generates a set of traces by iteratively invoking a model checker. The method mitigates the memory consumption problem by dynamically building partitions along the traces. This method was applied to a testability case study, and it generated the complete trace set, while ordinary model-checking could only generate 26%.