This paper gives an overall description of CRIM's ATIS (Air Travel Information System) natural language speech understanding system, with special emphasis on the speech recognition component. This spontaneous speech recognizer is used to generate the N-best sentence hypotheses which are needed by our natural language component in order to interpret the spoken sentence. This interpretation is then converted into an SQL query which is used to generate the desired answer from the relational database. The words in the system's vocabulary are built from a set of context-dependent phonetic HMMs. We use discrete HMMs with 4 codebooks, one for each of the following parameter sets: mel cepstral coefficients and energy, as well as their derivatives. We describe our training procedure for both the HMMs and the language model. Despite having only recently started working on large-vocabulary tasks, we feel that we should soon be able to bring our system's recognition performance (now around 82% word correct) to a level comparable to that of the other sites working on the ATIS task.