We estimate the number and
ratio of negative homothetic copies of a d-dimensional convex body C sufficient for
the covering of C. If the number of those copies is not very large, then our estimates
are better than recent estimates of Rogers and Zong. Particular attention is paid to
the 2-dimensional case. It is proved that every planar convex body can be
covered by two copies of ratio − (this ratio cannot be lessened if C is a
triangle).