Observability analysis based exclusively on topological information may lead to systems whose state cannot be estimated by regular state estimation methods. This paper discusses some practical situations in which the presence of the so called discardable measurements may pus undetected by topological observability analysis. As a consequence, wrong results, or even convergence problems, may occur. A numerically based observability analysis procedure is suggested for handling such cases; the new technique is an extension of previously published work on numerical observability analysis. The technique is fully illustrated by small scale examples taken from a real-life system where difficulties with discardable measurements have been observed.7313331340