In this paper we present factorized test generation techniques that can be used to generate test cases from a specification that is modelled as a labelled transition system. The test generation techniques are able to construct a sound (and complete) test suite for correctness criterion miocoF [5] by splitting up this correctness criterion into many simpler correctness criteria, and by generating tests for these simpler correctness criteria. By isolating the relevant part of the specification that is needed to generate tests for each of these simpler correctness criteria and using this part to generate tests from, test generation can be done more efficiently. These techniques are intended to keep the generation of tests from a specification feasible and manageable.