We consider algorithms for group testing problems when nothing is known in advance about the number of defectives. Du and Hwang suggested measuring the quality of such algorithms by its so-called (first) competitive ratio (see the Introduction). Later, Du and Park suggested a second kind of competitive ratio. For each kind of competitiveness, we improve the best-known bounds: in the first case, from 1.65 to $1.5+\ep$, and in the second from 16 to 4.