In this paper, we attempt to validate the flexible vocabulary approach for speaker independent isolated word and connected words recognition. We compare the performance of classical whole word HMMs against different sets of subword units. For this purpose, we model phonemes, diphones and words of the (Swiss) French language. The recognition rates obtained with phoneme models are monitored as we increase the amount of training data. The results of the described experiments validate the flexible vocabulary approach and show advantages and disadvantages of both proposed subword units against common whole word HMMs.