This paper summarizes the main results from the Speaker Verification (SV) research pursued so far in the CAVE project. Different state-of-the art SV algorithms were implemented in a common HMM framework and compared on two databases : YOHO (office environment speech) and SESP (telephone speech). This paper is concerned with the different design issues for LR-HMM-based SV algorithms which emerged from our investigations and which led to our current SV system, which delivers Equal Error Rates below 0.5 \% on a very realistic telephone speech database.