The semblance criterion widely used for slowness estimation is examined using the theory of statistical hypothesis testing and shown to be equivalent to that for detecting propagating signals of any energy at a specified slowness. We propose to suppress weak collar arrivals on semblance maps for logging while drilling (LWD) data by incorporating a minimum signal energy threshold in the aforementioned theory and using it to derive a couple of modifications of the semblance. Other simpler modification inspired by these are also proposed on heuristic grounds. All proposed modifications perform comparably on real LWD data and are effective at suppressing weak unwanted arrivals while preserving the desired ones.