In previous work, we have proposed a framework for black-box conformance testing of real-time systems based on timed automata specifications and two types of tests: analog-clock or digital-clock. Our algorithm to generate analog-clock tests is based on an on-the-fly determinization of the specification automaton during the execution of the test, which in turn relies on reachability computations. The latter can sometimes be costly, thus problematic, since the tester must quickly react to the actions of the system under test. In this paper, we provide techniques which allow analog-clock testers to be represented as deterministic timed automata, thus minimizing the reaction time to a simple state jump. We also provide a method for (statically) generating a suite of digital-clock tests which covers the specification with respect to a number of criteria: location, edge or state coverage. This avoids having to generate too many tests. We illustrate the benefit of the technique on a small example.