The steadily growing amount of orbital debris increases the probability and amount of collisions between two objects in orbit about the Earth. These collisions in turn create even more debris, and it is therefore important to keep track of future conjunctions. The U.S. Space Surveillance Network (SSN) uses ground- and space-based sensors to observe and track objects of about 10 cm and larger, of which the orbital information is coded in Two-Line Element (TLE) sets and listed in a catalog currently containing about 20,000 objects, which is partly distributed to the public. Using this TLE data, the Simplified General (and Deep-space) Perturbations 4 (SGP4/SDP4) analytical propagator is used to propagate the orbits of these objects, and includes secular, long-period and short-period perturbations due to the Earth's gravity field including J2, J3 and J4 and resonance effects for 12- and 24-hr orbits, as well as perturbations due to atmospheric drag, solar radiation, and gravitational attraction of the Sun and the Moon. The propagated orbits are used to predict conjunctions of pairs of objects. However, due to the large and increasing amount of objects in the catalog, numerically analysing all pairs would be too time-consuming. Therefore, numerous fast filters and sieves were designed to limit the search space of conjunction analysis, by discarding object pairs that are proven to never be able to conjunct. Four implementations of the classical perigee-apogee filter, next to six sieves with a new fine conjunction detection method, were analysed, implemented, and tested in terms of performance. The filter makes use of the altitude band of an object, and can be applied pre-hand. A method based on minimum and maximum radius determined from ephemerides, was found to be the most accurate and reliable in long-term application, while being able to be fine-tuned to the performance needs of a conjunction analysis process. Increasingly complex sieves are subsequently applied to the ephemerides at each time instance in a time interval, in order to efficiently discard object pairs. Eight possible improvements to the underlying theory and application of these sieves were made, resulting in one optimal combination of these improvements, and eventually resulting in a conjunction analysis system that is almost three times as fast as the best found reference method.